Theorem 10.2 : The lengths of tangents drawn from an external point to a circle are equal.
Given: Let circle be with centre O and P be a point outside circle PQ and PR are two tangents to circle intersecting at point Q and R respectively.
To Prove: Lengths of tangents are equal
i.e. PQ = PR
Construction: Join OQ, OR and OP
Proof: Now in right triangles OQP and ORP,
OQ = OR (Radii of the same circle)
OP = OP (Common)
And, ∠PRO = ∠PQR (90°)
Therefore, Δ OQP ≅ Δ ORP (RHS)
This gives PQ = PR (CPCT)