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Geometry Problem 789: Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line.
In triangle ABC, where angle B is a right angle, draw the altitude BH and the angle bisector BD of angle HBC. Let the incircle, with a radius of r, be tangent to side AC at point E. Our objective is to prove that DE is equal to r.
Right angle triangle,
Altitude and bisector,
Incircle's sweet touch.
DE equals r, proof shines bright,
Geometry's elegant light. |