Question 5
A quadrilateral $ABCD$ is circumscribed about a circle $(O)$. Let $M,N,P,Q$ be its points of tangency with the sides $AB,BC,CD,DA$, respectively. Let $I=NQ\cap AC$.
a) Prove that $\dfrac{IA}{IC}=\dfrac{QA}{NC}$.
b) Prove that the four lines $AC,BD,MP,NQ$ are concurrent.
a) Prove that $\dfrac{IA}{IC}=\dfrac{QA}{NC}$.
b) Prove that the four lines $AC,BD,MP,NQ$ are concurrent.