VTMO 2026 - Grade 9 - Final - SET 6 - Self-study Question 1

Triangle $ABC$ has $AB=5$, $AC=7$, and $BC=8$. Let $I$ be its incentre.

a) Find the inradius $r$.

b) Points $M,N$ lie on $BC,AC$ with $BM=5$ and $AN=5$. Lines $AM,BN$ meet at $K$. Prove that $K$ lies on the incircle of $ABC$.