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Geometry: Cyclic Quadrilateral Theorem
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Cyclic Quadrilateral: Theorem

Theorem:
If one side of the cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle.
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Cyclic Quadrilateral Theorem
Example: ABCD is a cyclic quadrilateral. AB and DC are produced to meet in E. Prove that
EBC ~ EDA.
Solution: In triangles EBC and EDA, you have


EBC = EDA ...[Exterior angle in a cyclic quad. is equal to opposite interior angle]
ECB = EAD ...[Exterior angle in a cyclic quad. is equal to opposite interior angle]
and, E = E ...[Common]
So, by AAA criterion of similarity, you have
EBC ~ EDA.
 
   
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