# Tangent bisectors

Geometry Level 5

In a triangle $$ABC$$, $$BK$$ is an angle bisector. A circle with radius $$\frac{5}{3}$$ passes through the vertex $$B$$, intersects $$AB$$ at a point $$L,$$ and is tangent to $$AC$$ at $$K$$. It is known that the length of $$AC$$ is $$3\sqrt{3},$$ and the ratio of the lengths $$|AK|$$ to $$|BL|$$ is $$6:5$$. The area of the triangle $$ABC$$ can be written as $$\frac{a\sqrt{b}}{c}$$, where $$a$$ and $$c$$ are coprime positive integers, and $$b$$ is not divisible by the square of any prime. What is the value of $$a+b+c$$?

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