Difference between revisions of "Two Tangent Theorem"
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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> | ||
− | + | == Proofs == | |
+ | === Proof 1 === | ||
+ | Since <math>OBP</math> and <math>OAP</math> are both right triangles with two equal sides, the third sides are both equal. | ||
+ | |||
+ | === Proof 2 === | ||
+ | From a simple application of [[Power of a Point]], the result follows. | ||
{{stub}} | {{stub}} | ||
− | |||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 18:42, 10 March 2009
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 and
are both right triangles with two equal sides, the third sides are both equal.
Proof 2
From a simple application of Power of a Point, the result follows.
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