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Question

In the given circle with centre O, if the radius of the circle is 13 cm, OQ⊥PR and OQ = 5 cm. Find PR.

A
12 cm
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B
13 cm
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C
24 cm
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D
5 cm
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Solution

The correct option is C 24 cm
Given,
OQ⊥PR
Radius of the circle = OP = 13 cm
OQ = 5 cm

In △OPQ,
Using Pythagoras theorem,
(OP)2=(PQ)2+(OQ)2
(13)2=(PQ)2+(5)2
169=(PQ)2+25
∴ PQ = 12 cm

The perpendicular from the centre of a circle to a chord bisects the chord.
∴ PQ = QR

So, PR = PQ + QR
= 24 cm.

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