Power of a point theorem
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
$ $===Case 2 (Outside the Circle):===
=====Classic Configuration=====
Given lines$ (Error compiling LaTeX. Unknown error_msg) AB CB
A
C
B
F
G
BF\cdot BA=BG\cdot BC $=====Tangent Line=====
Given Lines$ (Error compiling LaTeX. Unknown error_msg) AB AC
AC
C
A
AB
A
B
D
AD\cdot AB=AC^{2} $===Case 3 (On the Border/Useless Case):===
If two chords,$ (Error compiling LaTeX. Unknown error_msg) AB AC
0
0 $.