Question

A point P is 10 cm away from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to ____.

• A. 4 cm
• B. 5 cm
• C. 6 cm
• D. 3 cm

Answer 1

The correct option is C

6 cm

Given that OP = 10 cm, PQ = 8 cm.

We know that line joining point of contact of tangent to centre of circle is perpendicular to tangent.

$\therefore \angle OQP={90}^0$

Applying Pythagoras theorem to triangle OPQ
${OQ}^2+{QP}^2={OP}^2$
${OQ}^2+8^2={100}^2$
${OQ}^2=100-64$
$=36$
$OQ=6cm$

Hence, radius of the circle is 6 cm.