question_answer

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

Answer:

Given, a circle with centre O from point P with tangents PQ and PR drawn.

To prove:           \[PQ=PR\]

Proof: In \[\Delta \text{ }PQO\] and \[\Delta \text{ }PRO\]

\[\angle PQO=\angle PRO=90\]

(Angle between radius and tangent)

\[OQ=OR\] (Radius)

\[OP\] is common

\[\therefore \] By R.H.S. congruence rule

\[\Delta \,PQO\cong \Delta \,PRO\]

\[PQ=PR\] (c.p.c.t.)                  Hence Proved.