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Two Chords and a 45 Degree Angle

Source: 2020 AMC 12B #12

February 6, 2020
AMC 12 BAMC 12AMC2020 AMC2020 AMC 12Bgeometry

Problem Statement

Let AB‾\overline{AB} be a diameter in a circle of radius 52.5\sqrt2. Let CD‾\overline{CD} be a chord in the circle that intersects AB‾\overline{AB} at a point EE such that BE=25BE=2\sqrt5 and ∠AEC=45∘.\angle AEC = 45^{\circ}. What is CE2+DE2?CE^2+DE^2?
<spanclass=′latex−bold′>(A)</span> 96<spanclass=′latex−bold′>(B)</span> 98<spanclass=′latex−bold′>(C)</span> 445<spanclass=′latex−bold′>(D)</span> 702<spanclass=′latex−bold′>(E)</span> 100<span class='latex-bold'>(A)</span>\ 96 \qquad<span class='latex-bold'>(B)</span>\ 98 \qquad<span class='latex-bold'>(C)</span>\ 44\sqrt5 \qquad<span class='latex-bold'>(D)</span>\ 70\sqrt2 \qquad<span class='latex-bold'>(E)</span>\ 100
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