Question

A point P is at a distance of 29 cm from the centre of a circle of radius 20 cm. Find the length of the tangent drawn from P to the circle.

Answer 1

Consider the figure 

We know that the tangent is perpendicular to the radius of a circle.

So, OPB is a right angled traingle, with ∠OBP = 90°

By using Pythagoras theorem in ΔOPB, we get

⇒ OB² + PB² = OP²

⇒ (20)² + PB² = (29)²

⇒ 400 + PB² = 841

⇒ PB² = 841 – 400 = 441

⇒ PB = `sqrt(441)`

⇒ PB = 21

So, length of the tangent from point P is 21 cm.