# Triangle proofs and formulas [closed]

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.

## closed as off-topic by Watson, Namaste, E. Joseph, Adam Hughes, LeucippusNov 30 '16 at 0:25

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• Welcome to MSE. It helped if you showed your attempts to solve those, and where you got stuck in particular. This is not a blank-cheque homework solving site. – dxiv Nov 29 '16 at 7:37
• OK. Here's my work for #1. So I basically took r= [ABC]/s and made it into a=pi[ABC]^2/s^2. Then I assigned arbitrary 3-4-5 to triangle ABC. I know that a is 1, but I don't know how to proceed from there. – jonyoung2002 Nov 29 '16 at 7:51
• For #2a I just arbitrarily assigned ABC to be equilateral. Then, I just added it and got 180, not sure if this is right though. – jonyoung2002 Nov 29 '16 at 7:54
• For #2b I again assigned ABC as an equilateral triangle, but then I realized that I have to prove it for all triangles, so now I don't know where/how to start. – jonyoung2002 Nov 29 '16 at 7:55
• is $h$ realy the hypotenuse? i think $h$ is the hight and $c$ the hypotenuse? – Dr. Sonnhard Graubner Nov 29 '16 at 7:56