Heptagon's fine, but!

Geometry Level 5

There's a regular heptagon \(ABCDEFG\) in the Cartesian plane with center of it's circumcircle at point \(J(8,8)\).

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.


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