Question

In the given figure, point P is 26 cm away from the center O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then, the radius of the circle is

(a) 10 cm 

(b) 12 cm 

(c) 13 cm 

(d) 15 cm

Answer 1

Correct answer is (a) 10 cm

Construction: Join OT.

We know that the radius and tangent are perpendicular at their point of contact In right triangle PTO

By using Pythagoras theorem, we have

PO² = OT² + TP²

\(\Rightarrow\) 26² = OT² + 24²

\(\Rightarrow\) 676 = OT² + 576

\(\Rightarrow\) TP² = 100

\(\Rightarrow\) TP = 10cm