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Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
In ΔB₂C₂D, ∠B₂ = 90° - B/2∠C₂ = 90° - C/2So ∠D = B/2 + C/2 = 90° - A/2
Let the incircle of ΔABC touch AB at X, AC at Y, and BC at Z.Note BX = BYand CY = CZ.Follows B1B2 // XY and C1C2 // YZ.Hence ∠B2DC2 = ∠ZYX = 90° - A/2