Question

Prove that the length of the tangent lines drawn from the outer point is equal​

Answer 1

Answer:

Step-by-step explanation:

Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.

To prove: PA = PB

Construction: 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.

Answer 2

Step-by-step explanation:

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.