Tangent drawn from a point P, touches the circle at Q. O is the centre of this circle. If PQ = 12 cm and OQ = 5 cm, then what is the value of OP?

Explanation

Given: Tangent drawn from a point P, touches the circle at Q. O is the centre of this circle. PQ = 12 cm and OQ = 5 cm, Concept used: 1. The radius and tangent of a circle at a point of contact is always perpendicular to each other. So the angle is 90°. 2. Pythagoras Theorem: Base2 + Perpendicular2 = Hypotenuse2 Calculation: According to the concept, Since ∠OQP is 90°, ΔPQO is a right-angled triangle. OP is the hypotenuse. Now, OP ⇒ OQ2 + P Q2 ​ ⇒ 52 + 122 ​ ⇒ 169 = 13 cm ​ ∴ The value of OP is 13 cm.