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common tangent of 3 circles - All-Russian MO 2001 Regional (R4) 11.3

Source:

September 26, 2024
geometrytangent

Problem Statement

Let ADAD be the angle bisector of triangle ABCABC, and let the line ℓ\ell touch circumcircles of triangles ADBADB and ADCADC at points MM and NN accordingly. Prove that the circle passing through the midpoints of the segments BDBD, DCDC and MNMN is tangent to the line ℓ\ell.
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