Question 95
Let $ABC$ be an acute triangle with circumcenter $O$. Let $P,Q$ be the intersections other than $A$ of the altitude from $A$ and the extended line $AO$, respectively, with the circumcircle of $ABC$.
a. Prove that angles $BAP$ and $QAC$ are equal.
b. Prove that triangles $BCP$ and $CBQ$ are congruent.
c. If $M,N$ are the midpoints of $AB,AC$, prove that the area of quadrilateral $ABPC$ is four times that of quadrilateral $AMON$.
a. Prove that angles $BAP$ and $QAC$ are equal.
b. Prove that triangles $BCP$ and $CBQ$ are congruent.
c. If $M,N$ are the midpoints of $AB,AC$, prove that the area of quadrilateral $ABPC$ is four times that of quadrilateral $AMON$.