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 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