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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 $\angle A=45^\circ$, $\angle B=90^\circ$, and $\angle C=450^\circ$, what is the measure of $\angle YZX$?

 Aug 14, 2023
 #1
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I think that angle C = 45° (rather than 450°)

 

 

D is the center of the incircle of ABC

Draw DY and DX

And YD = DX = BX = BY

So YDXB is a square, so angle YDX =  90°

And angle YZX  is an inscribed angle in the  incircle  that has 1/2 the measure of  central angle YDX

So angle YZX = (1/2)(90°) = 45°

 

cool cool cool

 Aug 14, 2023

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