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AIME 2025 I / Alex divides a disk into four quadrants with two perpendicular diameters…

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question

Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.

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task_id: 01ad4919-4f39-5ec8-8b30-260ecf9c1735
task_key: AIME2025~2dI--test--01ad4919-4f39-5ec8-8b30-260ecf9c1735
task_revision_id: 2
config / split: AIME2025-I / test

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