Question 13
1. In a non-equilateral triangle $A B C$, the sides $a, b, c$ form an arithmetic progression. Let $I$ and $O$ denote the incentre and circumcentre of the triangle respectively.
a. Prove that $I O$ is perpendicular to $B I$.
b. Suppose $B I$ extended meets $A C$ in $K$, and $D, E$ are the midpoints of $B C, B A$ respectively. Prove that $I$ is the circumcentre of triangle $D K E$.
a. Prove that $I O$ is perpendicular to $B I$.
b. Suppose $B I$ extended meets $A C$ in $K$, and $D, E$ are the midpoints of $B C, B A$ respectively. Prove that $I$ is the circumcentre of triangle $D K E$.