Difference between revisions of "Two Tangent Theorem"
(added proofs) |
Northstar47 (talk | contribs) m |
||
| (6 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
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 == | == Proofs == | ||
| Line 7: | Line 7: | ||
=== Proof 2 === | === Proof 2 === | ||
| − | From a simple application of [[Power of a Point]], the result follows. | + | From a simple application of the [[Power of a Point Theorem]], the result follows. |
| + | ==See Also== | ||
{{stub}} | {{stub}} | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
| + | [[Category: Theorems]] | ||
Latest revision as of 21:47, 5 December 2023
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>
Contents
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.
See Also
This article is a stub. Help us out by expanding it.
