Prove that the lenghts of tangents drawn from an external point to a circle are equal.
Asked by anusarika mohanty | 21st Dec, 2013, 07:22: PM
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.
Answered by | 21st Dec, 2013, 09:29: PM
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