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).
Geometric Art of Problem 1415: Sketching, Typography, using iPad
See also: Typography and poster of problem 1408.
Search gogeometry.com
Recent Additions
Geometry Problems
Ten problems: 1411-1420
Visual Index
Open Problems
All Problems
Triangle
Isosceles Triangle
Altitude
Circle
Incircle
Excircle
Tangent Line
Perpendicular lines
View or Post a solution