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same circumcircle and inscribed circles

Source:

September 18, 2010
geometrycircumcirclegeometry proposed

Problem Statement

Let ⊙O\odot O , ⊙I\odot I be the circumcircle and inscribed circles of triangleABCABC . Prove that : From every point DD on ⊙O\odot O ,we can construct a triangle DEFDEF such that ABCABC and DEFDEF have the same circumcircle and inscribed circles
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