Geometry Problem 1415: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle

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 triangle JBG is an isosceles triangle (BJ = BG).  

 

Geometry problem 1415: Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle, Tutoring
 


Geometric Art of Problem 1415: Sketching, Typography, using iPad

Geometric Art of Problem 1415: Sketching, Typography, using iPad, Tutor

 

See also: Typography and poster of problem 1408.

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