The triangle at the left of this figure is such that if the base is extended to the right, and a line is drawn through the apex such that it forms equal angles with the other two sides of the triangle, the length of the dashed line is 45.

There are infinitely many such triangles, however we will restrict ourselves to triangles with integer lengths. And we wish to find the smallest such triangle (either by area or by perimeter – it’s the same triangle).

Can you find it?