In a triangle ABC,
BK is an angle bisector. A circle with
radius 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√3, and the ratio of the lengths
|AK| to
|BL| is
6:5. The area of the triangle
ABC can be written
as a√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?
3 answers