What A triangle is inscribed in another figure if each vertex of the triangle touches that figure true or false?

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Description : a square is inscribed in an isosceles triangle so that the square and the triangle have one angle common. show that the vertex of the square opposite the vertex of the common angle bisect the hypotenuse. -Maths 9th

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Description : what- The Ferris wheel has forty spokes. The center of rotation is the vertex of each triangle.How many degrees does the Ferris wheel rotate from one gondola to the next?

Last Answer : 9 degrees

Description : A square is inscribed in an isosceles right triangle, so that the square and the triangle have one angle common. -Maths 9th

Last Answer : Given In isosceles triangle ABC, a square ΔDEF is inscribed. To prove CE = BE Proof In an isosceles ΔABC, ∠A = 90° and AB=AC …(i) Since, ΔDEF is a square. AD = AF [all sides of square are equal] … (ii) On subtracting Eq. (ii) from Eq. (i), we get AB – AD = AC- AF BD = CF ….(iii)

Description : A square is inscribed in an isosceles right triangle, so that the square and the triangle have one angle common. -Maths 9th

Last Answer : Given In isosceles triangle ABC, a square ΔDEF is inscribed. To prove CE = BE Proof In an isosceles ΔABC, ∠A = 90° and AB=AC …(i) Since, ΔDEF is a square. AD = AF [all sides of square are equal] … (ii) On subtracting Eq. (ii) from Eq. (i), we get AB – AD = AC- AF BD = CF ….(iii)

Description : What is the radius of a circle inscribed in a triangle having side lengths 35 cm, 44 cm and 75 cm? -Maths 9th

Last Answer : (d) 6 cmLet a = 35 cm, b = 44 cm, c = 75 cm. Thens = \(rac{a+b+c}{2}\) = \(rac{34+44+75}{2}\) cm = 77 cm∴ Area if triangle = \(\sqrt{77(77-35)(77-44)(77-75)}\) cm2= \(\sqrt{77 imes42 ... ) cm2 = 462 cm2∴ Radius of incircle = \(rac{ ext{Area}}{ ext{semi-perimeter}}\) = \(rac{462}{77}\) cm = 6 cm.

Description : If the area of a circle, inscribed in an equilateral triangle is 4π cm^2, then what is the area of the triangle? -Maths 9th

Last Answer : (a) 12√3 cm2Since area of circle = 4π ⇒ πr2 = 4π ⇒ r = 2 cmIn ΔOAD,tan 30° = \(rac{OD}{AD}\) ⇒ \(rac{1}{\sqrt3}\) = \(rac{2}{AD}\)⇒ AD = 2√3 cm ∴ AB = 2AD = 4√3 cm∴ Area of equilateral ΔABC = \(rac{\sqrt3}{4}\) (AB)2= \(rac{\sqrt3}{4}\) (4√3)2 = 12√3 cm2.

Description : A circle is inscribed in an equilateral triangle of side a. What is the area of any square inscribed in this circle? -Maths 9th

Last Answer : (c) \(rac{a^2}{6}.\)If a' is length of the side of ΔABC, thenArea of ΔABC = \(rac{\sqrt3}{4}\,a^2\)semi-perimeter of ΔABC = \(rac{3a}{2}\)∴ Radius of in-circle = \(rac{ ext{Area}}{ ext{semi-perimeter}}\) = \( ... {( ext{diagonal})^2}{2}\) = \(rac{\big(rac{a}{\sqrt3}\big)^2}{2}\) = \(rac{a^2}{6}.\)

Description : Find the area of an equilateral triangle inscribed in a circle circumscribed by a square made by joining the mid-points -Maths 9th

Last Answer : (d) \(rac{3\sqrt3a^2}{32}\)Let AB = a be the side of the outermost square.Then AG = AH = \(rac{a}{2}\)⇒ GH = \(\sqrt{rac{a^2}{4}+rac{a^2}{4}}\) = \(rac{a}{\sqrt2}\)∴ Diameter of circle = \(rac{a} ... rac{\sqrt3}{2}\) = \(rac{\sqrt3a^2}{32}\)∴ Area of ΔPQR = 3 (Area of ΔPOQ) = \(rac{\sqrt3a^2}{32}\)

Description : Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height? -Maths 9th

Last Answer : (b) 2 : 4 : 3.For an equilateral triangle of side a units,In-radius = \(rac{a}{2\sqrt3}\) units⇒ Diameter of inscribed circle = \(rac{a}{\sqrt3}\) unitsCircumradius = \(rac{a}{\sqrt3}\)⇒ Diameter of circumscrible circle = \( ... \(rac{2a}{\sqrt3}\): \(rac{\sqrt3}{2}a\) = 2a : 4a : 3a = 2 : 4 : 3.

Description : In the diagram AB and AC are the equal sides of an isosceles triangle ABC, in which is inscribed equilateral triangle DEF. -Maths 9th

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Description : A rectangle inscribed in a triangle has its base coinciding with the base b of the triangle. If the altitude of the triangle is h, and the -Maths 9th

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Last Answer : I determined and what next? A circle inscribed in a triangle This is a circle that touches all sides of the triangle. The center of the circle inscribed in the triangle ABC is the intersection of the axes of the ... the 2nd series of the summer part of KMS 2009 / 2010.pdf example no.6" in Slovak

Description : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of the triangle is maximum when `theta=pi

Last Answer : An isosceles triangle of vertical angle `2theta` is inscribed in a circle of radius `a` . Show that the area of ... pi/4` C. `pi/6` D. None of these.

Description : Is the shortest distance from the center of the inscribed circle to the triangle sides is the circles?

Last Answer : It is its inradius.

Description : In the following figure a wire bent in the form of a regular polygon of `n` sides is inscribed in a circle of radius `a`. Net magnetic field at centre

Last Answer : In the following figure a wire bent in the form of a regular polygon of `n` sides is inscribed in a circle of ... (ni)/(a)mu_(0)tan.(pi)/(n)` D.

Description : The centroid of a triangle is at the inter-section of a.perpendicular bisectors b.107 dynes c.base and perpendicular from opposite vertex d.perpendiculars down from the corners e.medians

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Description : If the distance from the vertex to the centroid of an equilateral triangle is 6 cm, then what is the area of the triangle? -Maths 9th

Last Answer : (b) 27√3 cm2.Let G be the centroid of ΔPQR. Then, PG = 6 cm.Now, \(rac{PG}{GS}\) = \(rac{2}{1}\) ⇒ GS = 3 cm∴PS = PG + GS = 9 cm (i)∴ If a is the length of a side of ΔPQR, then ... = 6√3 cm∴ Area of equilateral ΔPQR = \(rac{\sqrt3}{4}\) (a)2= \(rac{\sqrt3}{4}\) x (6√3)2 cm2 = 27√3 cm2.

Description : In a triangle, the ratio of the distance between a vertex and the orthocentre and the distance of the circumcentre from the side -Maths 9th

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Description : Prove that any straight line drawn from the vertex of a triangle to the base is bisected by the straight line which -Maths 9th

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Description : The area of a triangle is 5. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y) -Maths 9th

Last Answer : Let A(x1, y1) = (3, 4), B(x2, y2) ≡ (0, 5), C(x3, y3) ≡ (2, -1)and D(x4, y4) ≡ (3, -2) be the vertices of quadrilateral ABCD.Area of quad. ABCD = \(rac{1}{2}\) |{(x1 y2 - x2 y1) + (x2y3 - x3y2) + (x3y4 - x4y3) ... ) + (12 + 6)}|= \(rac{1}{2}\) |{15 - 11 + 0 + 18}| = \(rac{1}{2}\)x 22 = 11 sq. units.

Description : The two vertices of a triangle are (2, –1), (3, 2) and the third vertex lies on the line x + y = 5. The area of the triangle is 4 units. -Maths 9th

Last Answer : (c) (5, 0) or (1, 4) Let the third vertex of the triangle be P(a, b). Since it lies on the line x + y = 5, a + b = 5 ...(i) Also, given area of triangle formed by the points (2, -1), (3, 2) and (a, b) = 4 ... b) - (-3a + b) = 5 + 15⇒ 4a = 20 ⇒ a = 5 ⇒ b = 0. ∴ The points are (1, 4) and (5, 0).

Description : If A (-2, 4), B (0, 0) and C (4, 2) are the vertices of triangle ABC, then find the length of the median through the vertex A. -Maths 9th

Last Answer : D=slid ht of BC D≅(20+4​,20+2​) =(2,1) ∴ Length of median = Light of AD =root(−2−2)2+(4−1)2​=root42+32​=5 hope it helps thank u

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Description : Which term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite sideso that the line segment is perpendicular to that line?

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Description : Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC. -Maths 9th

Last Answer : Weknowthatthediagonalofaparallelogram(∥gm)dividesitintotwocongruenttriangles.SoAreaof∥gmABCD=2 Areaof△BCD.AccordingtoHeron′sformulathearea(A)oftrianglewithsidesa,b&cisgivenasA=2[s(s−a)(s−b) ... 90=180Areaof∥gm=base heightHeightofaltitudefromvertexAonsideCDoftheof∥gm=baseCDareaof∥gmABCD =12180 =15cm

Description : Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC. -Maths 9th

Last Answer : =3 x 3 x 5 x 2 cm2 Area of parallelogram ABCD = 2 x 90 = 180 cm2 (ii) Let altitude of a parallelogram be h. Also, area of parallelogram ABCD =Base x Altitude ⇒ 180 = DC x h [from Eq. (ii)] ... h ∴ h = 180/12= 15 cm Hence, the area of parallelogram is 180 cm2 and the length of altitude is 15 cm.

Description : The ellipse `x^2+""4y^2=""4` is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes t

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Description : Consider a Hamiltonian Graph (G) with no loops and parallel edges. Which of the following is true with respect to this Graph (G) ? (a) deg(v) ≥ n/2 for each vertex of G (b) |E(G)| ≥ 1/2 (n-1)(n-2)+2 edges (c) deg(v) + deg( ... edge (A) (a) and (b) (B) (b) and (c) (C) (a) and (c) (D) (a), (b) and (c)

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Description : Scaling of a polygon is done by computing a.The product of (x, y) of each vertex b.(x, y) of end points c.Center coordinates d.Only a

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Description : Polygons are translated by adding to the coordinate positionof each vertex and the current attribute setting. a.Straight line path b.Translation vector c.Differences d.Only b

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Description : We are three brothers, running behind each other. Always running round our mother: one after the other, yet no matter how fast we run, we never touches each other. What are we? -Riddles

Last Answer : Fan blades.

Description : Not far off shore a ship stands with a rope ladder hanging over her side. The rope has 10 rungs. The distance between each rung is 12 inches. The lowest rung touches the water. The ocean is calm. ... hour. How soon will the water cover the third rung from the top rung of the rope ladder? -Riddles

Last Answer : When a problem deals with a physical phenonmenon, the phenonmenon should be considered as well as the numbers given. As the water rises, so does the rope ladder. The water will never cover the rung.

Description : If three cylinders of radius r and height h are placed vertically such that the curved surface of each cylinder touches the curved surfaces -Maths 9th

Last Answer : hr2 (3-√−π2)(3−π2) The bases of the three cylinders when placed as given are as shown in the figure : Let the radius of the base of each cylinder = r cm. We are required to find the volume of air. ... ∠C = 60º) = 3 x 60o360o πr2=πr2260o360o πr2=πr22 ∴ Required volume = (3-√r2−π2r2)h=(3-√−π2)r2h.

Description : Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a units. -Maths 9th

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Description : Prove that the curve `y^2=4x and x^2 +y^2 - 6x +1=0` touches each other at thepoint `(1, 2),` find the equation of the common tangents.

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Description : A directed graph is ………………. if there is a path from each vertex to every other vertex in the digraph. A) Weakly connected B) Strongly Connected C) Tightly Connected D) Linearly Connected

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Description : A vertex cover of an undirected graph G(V, E) is a subset V1 ⊆ V vertices such that (A) Each pair of vertices in V1 is connected by an edge (B) If (u, v) ∈ E then u ∈ V1 and v ∈ V1 (C) If (u, v) ∈ E then u ∈ V1 or v ∈ V1 (D) All pairs of vertices in V1 are not connected by an edge

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Description : A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. -Maths 9th

Last Answer : Each shade of paper is divided into 3 triangles i.e., I, II, III 8 cm For triangle I: ABCD is a square [Given] ∵ Diagonals of a square are equal and bisect each other. ∴ AC = BD = 32 cm Height of AABD ... are: Area of shade I = 256 cm2 Area of shade II = 256 cm2 and area of shade III = 17.92 cm2

Description : The figure shows the front view of a convex lens, which originally had only one edge. Five holes of different shapes, namely triangle, square, pentagon, hexagon and circle, were drilled through it at points P ... . What is the total number of edges in the lens after the holes were drilled? 

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Description : Triangle P and pentagon Q have markings on them as shown in the figure. If they are placed over each other, which of the following arrangements is/are possible? 

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Description : Marking mortal privation, when firmly in place. An enduring summation, inscribed in my face.What am I? -Riddles

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Description : If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

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Description : If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

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Description : In a sphere of radius 2 cm a cone of height 3 cm is inscribed. What is the ratio of volumes of the cone and sphere ? -Maths 9th

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Description : A trapezium ABCD in which AB || CD is inscribed in a circle with centre O. Suppose the diagonals AC and BD of the trapezium intersect at M -Maths 9th

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Description : “Proclaim Liberty Throughout All the Land Unto All the Inhabitants thereof” inscribed on the

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Description : In the 3rd century BC, the rule of which ruler is inscribed in Brahmi script ?

Last Answer : Ashoka's reign is inscribed in Brahmi script in the 3rd century BC.

Description : What is the angle of the circle or the angle inscribed in the circle ?

Last Answer : If the vertex of an angle is a point in a circle and there is a point in a circle in addition to the vertex on each side of a circle, then the angle is called a circle angle or an angle inscribed in the circle.

Description : A circle is inscribed in a polygon. As the number of sides increases, the difference in areas of circle and polygon _________.

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Description : If two chords intersect inside a circle the angles formed are called inscribed angles.?

Last Answer : yes