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

5 cm

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24 cm

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13 cm

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12 cm

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Solution

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

In △OPQ,
Using Pythagoras theorem,
$(O P)^{2} = (P Q)^{2} + (O Q)^{2}$
$(13)^{2} = (P Q)^{2} + (5)^{2}$
$169 = (P Q)^{2} + 25$
∴ 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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