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Given △ABC, extend sides AB and AC to rays AB and AC forming exterior angles. Let...

Given △ABC, extend sides AB and AC to rays AB and AC forming exterior angles. Let the line rA be the angle bisector ∠BAC, let line rB be the angle bisector of the exterior angle at B, and let line rC be the angle bisector of the exterior angle at C.

• Prove that these three rays are concurrent; that is, that they intersect at a single point. Call this point EA

• Prove that EA is the center of a circle which is tangent to the extended sides of the triangle.

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