MathNet 2010 — Part 06 Question 167

In a triangle $ABC$ on the side $AC$ the points $F$ and $L$ with $AF = LC \lt \frac{1}{2}AC$ are chosen. Find an angle $FBL$, if $AB^2 + BC^2 = AL^2 + LC^2$.

**Answer:** $\angle FBL = 90^\circ$.