Minimum Perimeter of a triangle

Question

I have been playing the app Euclidea, I have been doing quite well but this one has me stumped.

"Construct a triangle whose perimeter is the minimum possible whose vertices lie on two side of the angle and the third vertex is at point a"

see image >> minimum perimeter

I think the solution may have something to the Problem of Apollonius, but I cant quite wrap my head around it.

Any help much appreciated.

Answer 1

Reflect the point $A$ in each of the two lines to get points $A_1,A_2$. Let the line $A_1A_2$ meet the two lines at $B,C$. The required triangle is $ABC$.