# 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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