Problem

Holiday Contest 2025 - Team Round - Problem 17

On the coordinate plane, let $A$ , $B$ , and $C$ be points the distance from the origin to each of these points is $25$ . Denote $H$ as the orthocenter of $\triangle ABC$ . If the sum of the coordinates of $A$ , $B$ , and $C$ are $31$ , $5$ , and $-25$ , respectively, find the sum of all possible values of the sum of the coordinates of $H$ .

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Problem Tags: 2-d Geometry

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Category: Holiday Contest
Points: 6
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