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. <geogebra>4f007f927909b27106388aa6339add09df6868c6</geogebra>

Proofs

Proof 1

Since $OBP$ and $OAP$ 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.

See Also

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