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