How to calculate a Circle Radius tangent to three lines?

Question

Need to calculate the radius of the circle, which is tangent to three lines with a given angle.

Answer 1

Hint: draw the radius of the circle, from the centre to the contact points. Use symmetry. You'll find the equation $$ \tan{\frac{99^{\circ}}{2}} = \frac{R}{\left( 5/2 \right)} $$