Geometry Problem 1298

Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint

The figure below shows an arbelos ABC (AB, BC, and AC are semicircles of centers O1, O2, and O). The incircle I of the arbelos is tangent to semicircles AC, AB, and BC at T, T1, and T2, respectively. The bisector of the angle ATC cuts the incircle at P and IP extended cuts AC at H. Prove that (1) IH is perpendicular to AC; (2) P is the midpoint of IH.


Geometry Problem 1298: Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint
 


Mosaic of problem 1298 in Motion using Mobile Apps, iPad

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