Machu Picchu, Geometry

Geometry Problem 1121:  Casey's Theorem. Generalized Ptolemy's Theorem. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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In the figure below, the circles A,B,C,D are tangent to the circle O; a, b, c, d, x, y are the common tangent to circles A and B, B and C, C and D, D and A, A and C, and B and D respectively. Prove the generalized Ptolemy's theorem:
x.y = a.c + b.d

 


Geometry problem 1121: Casey Theorem, Generalized Ptolemy

 

See also:

Euclidean Geometry

Ptolemy's Theorem.
 

Cyclic Quadrilateral: Ratio of the Diagonals
 

Brahmagupta's Theorem Cyclic quadrilateral.

Quadrilateral Index 

Quadrilaterals.

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Last updated: Jun 14, 2015 by Antonio Gutierrez.