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. 10cm
• B. 15cm
• C. 20cm
• D. 25cm

Answer 1

The correct option is D

25cm

Since tangent at a point on the circle is perpendicular to the radius to the point, we have $OP\perp OQ$.
Consider the figure below:

In the right angled triangle $\Delta$OPQ,

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

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

${OQ}^2=49+576$

${OQ}^2=625$

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