Difference between revisions of "Power of a point theorem"
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=====Tangent Line===== | =====Tangent Line===== | ||
| − | Given Lines <math> AB </math> and <math> AC </math> with <math> AC </math> tangent to the related circle at <math> C </math>, <math> A </math> lies outside the circle, and Line <math> AB </math> intersects the circle between <math> A </math> and <math> B </math> at <math> D </math>, <math> AD\cdot AB=AC^{2} </math> | + | Given Lines <math> AB </math> and <math> AC </math> with <math> AC </math> tangent to the related circle at <math> C </math>, <math> A </math> lies outside the circle, and Line <math> AB </math> intersects the circle between <math> A </math> and <math> B </math> at <math> D </math>, <math> AD\cdot AB=AC^{2} </math> |
====Normal Configuration==== | ====Normal Configuration==== | ||
Revision as of 14:46, 23 April 2024
Contents
Theorem:
There are three unique cases for this theorem. Each case expresses the relationship between the length of line segments that pass through a common point and touch a circle in at least one point.
Case 1 (Inside the Circle):
If two chords 
and 
intersect at a point 
within a circle, then 
Case 2 (Outside the Circle):
Classic Configuration
Given lines and 
originate from two unique points on the circumference of a circle (
and 
), intersect each other at point 
, outside the circle, and re-intersect the circle at points 
and 
respectively, then 
.
Tangent Line
Given Lines and 
with tangent to the related circle at , lies outside the circle, and Line intersects the circle between and at 
, 
Normal Configuration
Tangent Line
Case 3 (On the Border/Useless Case):
- Still working
