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

(Q 29 A – 30/2/1 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s start with a diagram for our better understanding:

Here, we have a circle with center O and radius r. 

P is an external point. From P, two tangents PA and PB are drawn which are touching the circle, at points A and B.

Step 2: Le’ts join O to A, O to B and O to P.

∠OAP and ∠OBP are both right angles (∵ tangent ⟂ radius)

∴  Δ OAP and Δ OBP are right angled triangles.

Let’s compare Δ OAP and Δ OBP

∵ OA = OB          (both are radii of same circle)

and OP = OP            (common side)

∴ by RHS criterion, Δ OAP ≅ Δ OBP

Step 3: Now, by CPCT, corresponding parts of congruent triangles are equal,

∴ PA = PB ……. Hence Proved !

Therefore, tangents drawn from an external point to a circle are equal.

Please press the “Heart” button if you like the solution.