Two Tangent Theorem: Difference between revisions
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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. | 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> | <geogebra>4f007f927909b27106388aa6339add09df6868c6</geogebra> | ||
Hello | |||
== Proofs == | == Proofs == | ||
=== Proof 1 === | === Proof 1 === | ||
Since < | Since <imath>OBP</imath> and <imath>OAP</imath> are both right triangles with two equal sides, the third sides are both equal. | ||
=== Proof 2 === | === Proof 2 === | ||
From a simple application of the [[Power of a Point Theorem]], the result follows. | From a simple application of the [[Power of a Point Theorem]](or [[Power Point Theorem]]), the result follows. | ||
==See Also== | ==See Also== | ||
Latest revision as of 22:32, 10 November 2025
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> Hello
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(or Power Point Theorem), the result follows.
See Also
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