Question 78
Let $ABC$ be a triangle, in which $m(\angle ABC) = 45^\circ$ and $m(\angle BAC) \gt 90^\circ$. Let $O$ be the midpoint of the side $[BC]$. We consider the point $M \in (AC)$ such that $m(\angle COM) = m(\angle CAB)$. The perpendicular through $M$ on $AC$ intersects the line $AB$ at the point $P$.
a) Find the measure of the angle $\angle BCP$.
b) Show that, if $m(\angle BAC) = 105^\circ$, then $PB = 2MO$.
a) Find the measure of the angle $\angle BCP$.
b) Show that, if $m(\angle BAC) = 105^\circ$, then $PB = 2MO$.