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AB + AT = TC - archimedes broken chord

Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P6

September 12, 2022
geometry

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC and MM the midpoint of the arc BCBC containing AA, plus TT the foot of the perpendicular from MM on side ACAC. Prove that AB+AT=TCAB + AT = TC. https://cdn.artofproblemsolving.com/attachments/0/a/5c90d7001f73c2f8ff2b0e69078f9a2a5cd606.png
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