# Triangle in a cyrcle

#### chiro

MHF Helper
Hey birkoof.

You have an isosceles triangle, a hemi-circle and another circle [in the top].

Try writing down as many variables as possible with your picture and show us the work you have done to write them as formulas so we can give you a hand.

#### birkoof

Well, inside the triangle I have 2alpha + beta = 180deg.
Using the Angle in the Center Theorem I get a X that is two times bigger than my beta (beta = x/2)
Implementing that in 2alpha + beta = 180deg i came with the result that alpha is equal to 90deg - x/4.
That's all i can get from the information given.

#### Idea

triangle with angles $$\displaystyle \beta ,\beta ,\alpha +\beta$$ says $$\displaystyle \alpha +3\beta =180{}^{\circ}$$

#### birkoof

triangle with angles $$\displaystyle \beta ,\beta ,\alpha +\beta$$ says $$\displaystyle \alpha +3\beta =180{}^{\circ}$$
Thanks, this helped a lot. Now i just express $$\displaystyle \beta$$ from the first triangle, which is $$\displaystyle 180{}^{\circ} - 2 \alpha$$ , put in the $$\displaystyle \alpha +3\beta =180{}^{\circ}$$ and i get that $$\displaystyle \alpha = 360{}^{\circ} /5$$ which is $$\displaystyle 72{}^{\circ}$$ and the right answer. Thanks!