Difference between revisions of "Power of a point theorem"

(Case 2 (Outside the Circle):)
(Case 2 (Outside the Circle):)
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===Case 2 (Outside the Circle):===
 
===Case 2 (Outside the Circle):===
  
**Classic Configuration**
+
__Classic Configuration__
  
 
**Tangent Line**
 
**Tangent Line**

Revision as of 12:54, 23 April 2024

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):

__Classic Configuration__

    • Tangent Line**

Normal Configuration

Tangent Line

Case 3 (On the Border/Useless Case):

    • Still working