Question 92
points $A$, $B$, $C$ Lie on a circle. line $PB$ Touches this circle at point $B$. Drop the Perpendiculars $PA_1$ and $PC_1$ from $P$ onto the lines $AB$ and $BC$, respectively (points $A_1$ and $C_1$ belong to segments $AB$ and $BC$, respectively). prove that $A_1C_1 \perp AC$. Let points $A$, $B$, $C$ lie on a circle, and a straight line $b$ touches this circle at the point $B$. From point $P$lying on a straight line $b$, perpendiculars are omitted $PA_1$ and $PC_1$ on straight lines $AB$ and $BC$ respectively (points $A_1$ and $C_1$ lie on the segments $AB$ and $BC$). Prove that $A_1C_1 \perp AC$. (L. Emelyanov)