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## Homework Statement

In triangle ABC, there is a maximun circle (3 intersection points) such that the lengths of the triangles are 3 : 4 : 5. A ray from the smallest angle C is tangential to the opposite side. Another ray from the greatest angle B is also tangential to the opposite side.

Find p : q where p is the length between the ray from the greatest angle to the tangential point and the intersection of this ray to another ray from smaller angle;

q is the length between the intersection of two rays and the vertex C.

## The Attempt at a Solution

The problem can be solved by Mass point geometry and areas/lengths.

However, I am not sure about the ratios of how the rays divide triangle's two sides.

We do know that whether the rays are bisectors although they meet inside the circle.

How would you solve the problem?