Power of a point theorem

Revision as of 13:53, 23 April 2024 by Sawyerj09 (talk | contribs)

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 $AB$ and $CD$ intersect at a point $P$ within a circle, then $AP\cdot BP=CP\cdot DP$

Case 2 (Outside the Circle):

[b]lassic Configuration[/b]

[b]Tangent Line[/b]

Normal Configuration

Tangent Line

Case 3 (On the Border/Useless Case):

    • Still working