Question 196
A straight line passing through the incenter $I$ of a triangle $ABC$ meets the sides $AB$ and $AC$ at points $P$ and $Q$ respectively. Let $BC = a$, $AC = b$, $AB = c$ and $\frac{PB}{PA} = p$, $\frac{QC}{QA} = q$.
a) Prove that $a(1+p)\vec{IP} = (a-pb)\vec{IB} - cp\vec{IC}$.
b) Prove that $a = bp + cq$.
c) Prove that if $a^2 = 4bcpq$, then the straight lines $AI$, $BQ$ and $CP$ are concurrent.
a) Prove that $a(1+p)\vec{IP} = (a-pb)\vec{IB} - cp\vec{IC}$.
b) Prove that $a = bp + cq$.
c) Prove that if $a^2 = 4bcpq$, then the straight lines $AI$, $BQ$ and $CP$ are concurrent.