CK12 - Geometry

The lengthsof the sidesof the trianglesatisfythe PythagoreanTheorem,so is perpendicularto
and is thereforetangentto the circle.

TangentSegmentsfroma CommonExternalPoint

TangentSegmentsfroma CommonExternalPointTheoremIf two segmentsfrom

the sameexteriorpointare tangentto the circle,then they are congruent.

Proof.

The figureaboveshowsa diagramof the situation.

• Given: is a tangentto the circleand is a tangentto the circle


• Prove:

Statement Reason

1. is tangentto the circle 1. Given


2. 
   
   
   
   2. Tangentto a CircleTheorem
   
   
   
   


3. is a tangentto the circle 3. Given


4. 
   
   
   
   4. Tangentto a CircleTheorem
   
   
   
   


5. 
   
   
   
   5. Radiiof samethe circle
   
   
   
   


6. 
   
   
   
   6. Sameline
   
   
   7. Hypotenuse-Legcongruence
   
   
   
   


7. 
   
   
   
   8. CongruentPartsof CongruentTrianglesare Con-
      gruent
   
   
   
   

8.