Question 151
Let $ABC$ be an isosceles right triangle with $\angle C = 90^{\circ}$. Let $X$ be a point on the line segment $AC$, and let $Y$ and $Z$ be, respectively, the feet of the perpendiculars from $A$ and $C$ to the line $BX$. Prove that
$$
BZ = YZ + AY
$$
$$
BZ = YZ + AY
$$