# Heptagon's fine, but!

**Geometry**Level 5

Every side of the heptagon is of length \(4 \sin \frac{\pi}{7}\).

Point \(H\) has coordinate \((16,12)\).

Find \(HA^2+HB^2+HC^2+HD^2+HE^2+HF^2+HG^2\).

**Details and assumptions**:

A regular heptagon has 7 vertices and all sides are of equal length.

The angle \(\frac{\pi}{7}\) is in radians.