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Circle $$\Gamma$$ is the incircle of $$\triangle ABC$$ and is also the circumcircle of $$\triangle XYZ$$. The point X is on $$\overline{BC}$$, the point Y is on $$\overline{AB}$$, and the point Z is on $$\overline{AC}$$. If $$\angle A=40^\circ$$$$\angle B=60^\circ$$, and $$\angle C=80^\circ$$, what is the measure of $$\angle YZX$$?

Note that it's YZX, not AYX

May 27, 2020

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Triangles CXZ and AYX are isosceles triangles;

Angle CZX = angle CXZ  =  55°                angle AZY = angle AYZ  = 70°

May 27, 2020