# You can't bash it out

Geometry Level 3

$$P$$ is a point on the base $$BC$$ of a $$\triangle(ABC)$$ and $$r_{1},r_{2},r_{3}$$ be the in-radii of the triangles $$ABC,ACP,ABP$$ respectively , $$h_{a}$$ is the length of altitude from $$A$$ to $$BC$$. Find $$h_{a}$$ given that $$r_{1}=5,r_{2}=3,r_{3}=4$$.

Bonus: Try to generalisze it.

×