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

**Question:**

In the given figure, point P is 26 cm away from the centre 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

**Solution:**

Construction: Join OT

We know that the radius and tangent are perperpendular at their point of contact

In right triangle PTO

By using Pythagoras theorem, we have

PO2 = OT2 + TP2

⇒ 262 = OT2 + 242

⇒ 676 = OT2 + 576

⇒ TP2 = 100

⇒ TP = 10 cm

Hence, the correct answer is option (a).