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locus wanted, semicircle, constant length (1998 Chile Level 2 P2)

Source:

June 17, 2020
geometryLocussemicircle

Problem Statement

Given a semicircle of diameter AB AB , with AB=2r AB = 2r , be CD CD a variable string, but of fixed length c c . Let E E be the intersection point of lines AC AC and BD BD , and let F F be the intersection point of lines AD AD and BC BC . a) Prove that the lines EF EF and AB AB are perpendicular. b) Determine the locus of the point E E . c) Prove that EF EF has a constant measure, and determine it based on c c and r r .
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