Prove that the lengths of tangents drawn from an external point to a circle are equal.

Given:

• Circle with centre A

• Tangents IB and IF

To Prove: IB = IF
Proof:

In ∆ ABI and ∆ AFI

• AB = AF = Radius of the circle

• ∠ ABI = ∠ AFI = 90°

(∵ tangents are perpendicular to the radius)

• AI = AI (common side)

So, by RHS rule, ∆ ABI ≅ ∆AFI

⇒ BI = FI
(∵ corresponding sides of congruent triangles are equal)

Hence, the lengths of tangents drawn from an external point to a circle are equal.