Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Tuesday, March 17, 2015
Geometry Problem 1100: Triangle, Circle, Centers, Vertex, Radius, Angle
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In ΔB₂C₂D,
ReplyDelete∠B₂ = 90° - B/2
∠C₂ = 90° - C/2
So ∠D = B/2 + C/2 = 90° - A/2
Let the incircle of ΔABC touch AB at X, AC at Y, and BC at Z.
ReplyDeleteNote BX = BYand CY = CZ.
Follows B1B2 // XY and C1C2 // YZ.
Hence ∠B2DC2 = ∠ZYX = 90° - A/2