Prove that tangent drawn from the exterior point of a circle are equal

1.	Prove that tangent drawn from the exterior point of a circle are equal length
Answer» Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.To prove: PA = PBConstruction: Join OA, OB, and OP.It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact. OA PA and OB PB ... (1)In OPA and OPB:OAP = OBP (Using (1))OA = OB (Radii of the same circle)OP = OP (Common side)Therefore, OPA OPB (RHS congruency criterion)PA = PB(Corresponding parts of congruent triangles are equal)Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.

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