Problem

Holiday Contest 2025 - Guts Round - Set 8 Problem 3

On the Cartesian plane, let $O$ be the origin and let $A\neq O$ be on $y=-x^2$ . Let the tangents from $A$ to $y=x^2$ intersect $y=x^2$ at $B$ and $C$ . If $\angle BOC = 45^\circ$ . The $y$ -coordinate of $A$ can be written as $a-\sqrt{b}$ for integers $a$ and non-square $b$ . Find $|100a|+|b|$ .

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Category: Holiday Contest Guts Round
Points: 7
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