Two Tangent Theorem

The two tangent theorem states that given a circle, if P is any point lying outside the circle, and if A and B are points such that PA and PB are tangent to the circle, then PA = PB.

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Proofs

Proof 1

Since and are both right triangles with two equal sides, the third sides are both equal.

Proof 2

From a simple application of the Power of a Point Theorem, the result follows.