Question 15
In triangle $ABC$, $M$ is the midpoint of $BC$. We draw the circle with centre $O$ that passes through the points $A$ and $C$ and is tangent to the line $AM$. The extension of $BA$ intersects the circle at $D$ and the extension of $CD$ intersects the extension of $MA$ at $P$, as shown in the diagram below. Prove that $OP\perp BC$.
Section B instruction: Show your detailed solution. Each question is worth 20 points.
Section B instruction: Show your detailed solution. Each question is worth 20 points.