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 17:42, 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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