Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the A distance between AB and CD is 6 cm, find the radius of the circle. -Maths 9th

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the A distance between AB and CD is 6 cm, find the radius of the circle. -Maths 9th
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  Join OA and OC. Let the radius of the circle be r cm and O be the centre  Draw OP⊥AB and OQ⊥CD.  We know, OQ⊥CD, OP⊥AB and AB∥CD.  Therefore, points P,O and Q are collinear. So, PQ=6 cm.  Let OP=x.  Then, OQ=(6–x) cm.  And OA=OC=r.    Also, AP=PB=2.5 cm and CQ=QD=5.5 cm. (Perpendicular from the centre to a chord of the circle bisects the chord.)    In right triangles QAP and OCQ, we have OA2=OP2+AP2 and OC2=OQ2+CQ2 ∴r2=x2+(2.5)2                 ..... (1)  and r2=(6−x)2+(5.5)2      ..... (2)  ⇒x2+(2.5)2=(6−x)2+(5.5)2 ⇒x2+6.25=36−12x+x2+30.25 12x=60 ∴x=5   Putting x=5 in (1), we get  r2=52+(2.5)2=25+6.25=31.25 ⇒r2=31.25⇒r=5.6 Hence, the radius of the circle is 5.6 cm
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Last Answer : b=2c=3​⇒⇒b=3​c=23​​cosA=2bcb2+c2−a2​⇒23​​=33+43​−a2​⇒233​​=415​−a2 ⇒a2=415​−43​​⇒a=1.673278 We know sinaa​=2R1​⇒R=2asina​=221​​=41​

In the above figure, O is the centre of the circle AB,AD and CD are the chords . If `/_ ADC=130^(@)` then fid `/_ ACB`.

Description : In the above figure, O is the centre of the circle AB,AD and CD are the chords . If `/_ ADC=130^(@)` then fid `/_ ACB`.

Last Answer : In the above figure, O is the centre of the circle AB,AD and CD are the chords . If `/_ ADC=130^(@)` then fid `/_ ACB`.