MathDB
2024 Team Problem 10

Source:

April 23, 2024
team

Problem Statement

Square ABCDABCD has side length 22. For each 0≤r≤20 \leq r \leq 2, point PrP_r is on side AB‾\overline{AB} with APr=rAP_r = r, and square Σr\Sigma_r is constructed with diagonal DPr‾\overline{DP_r}. Let region R\mathcal{R} be the set of all points that are in both Σ0\Sigma_0 and Σ2\Sigma_2, but not in Σr\Sigma_r for at least one value of rr. Find the area of the convex hull of R\mathcal{R}.
Proposed by Justin Hsieh
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