The lengths of tangents of drawn from an external point to a circle are equal.Proof: we are given a circle with centre
O, a point
P lying outside the circle and two tangents
PQ,PR on te circle from
P. We are required to prove that
P=PRFor this, we join OP,OQ and OR. Then ∠OQR and ∠ORP are right angles, because these are angles between the radii and tangents, and according to Theorem 10.1 they are right angles. Now in right triangles OQP and ORP