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
• B. 13 cm
• C. 24 cm
• D. 5 cm

Answer 1

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.