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# Triangle ABC is a right triangle with right angle at A. Suppose AX is an

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Triangle ABC is a right triangle with right angle at A. Suppose AX is an altitude of the triangle, AY is an angle bisector of the triangle, and AZ is a median of the triangle, and angle XAY=13. If X is on BY, then what is the measure of angle ZAC?

bbelt711  Aug 1, 2017
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Z is the circumcenter of Triangle ABC , so $$\angle YAZ = \angle XAY$$  (very useful fact in geometry). Thus also Triangle ZAC=0, then we have $$\triangle ABC \sim \triangle XAC \implies 2 \theta = ?$$