Question

Prove that length of two tangent segments to A circle drawn from an external point are equal.​

Answer 1

Answer:

Given: A circle with centre O and an external point P are given. AP and BP are the two tangents drawn from an external point P. Construction: Draw seg OA, seg OB and seg OP. Thus, the lengths of two tangent segments to a circle drawn from an external point are equal.

Answer 2

Answer:

It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact. Therefore triangle OPA is congruent to triangle OPB by RHS criterion. Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.