1) What is the ratio of the area of a right triangle to the area of its incircle in the form $\frac{a \pi r}{br+ch}$ where $r$ is the inradius of the triangle and $h$ is the hypotenuse of the triangle.
2a) Let $\bigtriangleup ABC$ be an acute triangle with orthocenter $H$. Evaluate $\angle BHC + \angle BAC$.
2b) Let $H^`$ be the reflection of $H$ over $BC$. Prove that $ABH^`C$ is cyclic.
For 2a) Firstly, A, M, H, N are con-cyclic. This makes the color shaded angles are equal in pairs.
Applying vertically opposite angles, the value of the required is then obvious.
For 2b) It is just the direct consequence of (2a).