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Question

In the given figure, O is the centre of the circle with radius 5 cm. OP and OQ are perpendiculars to AB and CD respectively. AB = 8 cm and CD = 6 cm. Determine the length of PQ.


Solution

Given: Radius = 5 \ cm, \ OP \perp AB \ and \ OQ \perp CD

AB = 8 \ cm \ and \ CD = 6 \ cm

P \ and \  Q  are mid point of AB \ and \  CD respectively (\perp  from the center to a chord will bisect the chord)

d1In \triangle OAP

OA^2= OP^2+AP^2

25 = OP^2 + 16 \Rightarrow OP = 3 \ cm

Similarly, in \triangle OCQ

OC^2= OQ^2+CQ^2

25 = OQ^2+9 \Rightarrow OQ = 4 \ cm

Hence PQ = OP + OQ = 3 + 4 = 7 \ cm

\\


Mathematics
Concise Mathematics
Standard X

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