# Right Triangles In Regularity (Advanced 1)

**Geometry**Level 4

**RIGHT**angle \(\angle{MKN}\) inside with two intersections \(M\) and \(N\) with \(AB\) and \(BC\), respectively.

Given \(AM=6\) and \(CN=\frac{4}{5}\), so that \(MN\) can be found in length as \(\dfrac{b}{a}\sqrt{c}\) with \(a\) and \(b\) coprime positive integers and \(c\) square-free. Also we can find \(AC\) in length as a positive integer \(d\).

Find \(a+b+c+d\).