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

Click on the figure below.

 

Geometry Problems
1291-1300
Visual Index
Open Problems
All Problems
Arbelos
Triangle
Circle
Semicircle
Tangent Circles
Incircle
Angle Bisector
Angle
Perpendicular lines
Midpoint


View or Post a solution


 

 

Follow our magazine for
daily inspiration straight
to your Flipboard:

View my Flipboard Magazine.