# Problem 5. (3 points)

In triangle $A B C$, the midpoints of sides $A B=40$ and $B C=26$ are marked as points $K$ and $L$ respectively. It turns out that the quadrilateral $A K L C$ is a tangential quadrilateral. Find the area of triangle $A B C$.
# Answer: 264

## Solution:

According to the Midline Theorem, $K L=\frac{1}{2} A C$. In a cyclic quadrilateral, the sums of the opposite sides are equal, that is, $K L+A C=A K+C L=\frac{A B+B C}{2}$, so $\frac{3 A C}{2}=\frac{66}{2}$ and $A C=22$. Knowing the sides of the triangle, the area can be calculated using Heron's formula.

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