# Circles, Tangents, And Triangles (Oh My...)

Geometry Level 5

The red circle has radius 3 and the blue circle has radius 4. The tangents to one of their points of intersection, $$P_1,$$ are perpendicular.

The green circle is centered at the other point of intersection, $$P_2,$$ and passes through $$P_1.$$ It also intersects the red and blue circles at $$P_3$$ and $$P_4,$$ respectively.

What is the length of the altitude from $$P_1$$ in triangle $$P_1P_3P_4?$$

×