# A Strange Star in a Strange Shape

Geometry Level 3

A strange shape can be made by joining two semi-ellipses with same major axis, but different minor axes. The above image is an example of one such shape. The blue region is a semi-ellipse with semi-minor axis $$(OA)$$ of length $$3$$. The pink region is a semi-ellipse with semi-minor axis $$(OE)$$ of length $$4$$. The major axis $$(GC)$$, common to both semi-ellipses has a length of $$10$$.

Now, a $$7$$ - pointed star in inscribed in this strange shape, symmetric about line $$AE$$, such that $$BH$$ is parallel to major axis, $$\angle H = 90^{\circ}$$, and line $$GC$$ bisects angles $$\angle C$$ and $$\angle G$$.

Calculate $$\angle A + \angle B + \angle C + \angle D + \angle F + \angle G + \angle H$$.