If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD. -Maths 9th

1 Answer

Answer :

Let AXB and CYD are arcs of circle whose centre and radius are O and r units, respectively. Hence, the ratio of AB and CD is 1:1.

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Description : If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD. -Maths 9th

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Last Answer : ∴ ∠CAO = ∠ODB = x [angles in same segment ] ---- (i) Now, in right angled ΔDOB , ∠ODB + ∠DOB + ∠OBD = 180° ⇒ x + 90° + y =180° (using equation i) ⇒ x + y = 90°

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Last Answer : O Join AC and BD. Given, COB is the diameter of circle. ∠CAB = ∠BDC = 90° [angle in a semi-circle] Also, AB II CD ∠ABC = ∠DCB (alternate angles] Now, ∠ACB = 90° - ∠ABC and ∠DBC = 90° - ∠DCB = ... = ∠DBC BC = BC [common sides] ΔABC = ΔDCB [by ASA congruency] ∴ AC = BD [by CPCT] Hence Proved.

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Description : Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ . -Maths 9th

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Description : ABCD is a trapezium in which AB II CD and AD = BC (see flg). Show that: -Maths 9th

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