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IM bisects segment AD, incircle related

Source: Switzerland - Swiss MO 2009 p5

July 17, 2020
geometrybisects segmentincenterincircle

Problem Statement

Let ABCABC be a triangle with AB≠ACAB \ne AC and incenter II. The incircle touches BCBC at DD. Let MM be the midpoint of BCBC . Show that the line IMIM bisects segment ADAD .
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