Question

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

• A. 10 cm
• B. 15 cm
• C. 20 cm
• D. 25 cm

Answer 1

The correct option is D

25 cm

Since tangent at a point on the circle is perpendicular to the radius through that point of contact.

$\therefore OP\perp OQ$

$\text{In right angled triangle OPQ,}$

${OQ}^2={OP}^2+{PQ}^2\text{(By Pythagoras theorem)}$

${OQ}^2=7^2+{24}^2$

${OQ}^2=49+576$

${OQ}^2=625$

$OQ=\sqrt{625}=25cm$