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 $\angle YZX$?
+129771 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°
