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Convex Heptagon and Circular Sectors

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August 8, 2024
geometry2022

Problem Statement

Let HOPKINSHOPKINS be an irregular convex heptagon (i.e., its angles and side lengths are all distinct, with the angles all having measure less than 180āˆ˜180^{\circ}) with area 18761876 such that all of its side lengths are greater than 55, OP=20OP=20, and KI=22KI=22. Arcs with radius 22 are drawn inside HOPKINSHOPKINS with their centers at each of the vertices and their endpoints on the sides, creating circular sectors. Find the area of the region inside HOPKINSHOPKINS but outside the sectors.
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