Geometry Problem 1416: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle

Proposition

The figure below shows a right triangle ABC (angle B = 90 degree) with the altitude BH. The incircle I is tangent to BC at D. The excircle E corresponding to BC is tangent to BC at G and tangent to the extension of AB at F. FD extended and BH meet at J. Prove that the measure of the angle FJG is 45 degree.
 

Geometry problem 1416: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle, Tutoring

 


Geometric Art of Problem 1416: Sketching, Typography, iPad Apps

Geometric Art of Problem 1416: Sketching, Typography, iPad Apps, SW, Tutor

See also: Typography and poster of problem 1408.