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triangle construction given 2 midpoints 1989 Kyiv City MO 7.3

Source:

July 17, 2021
geometryconstruction

Problem Statement

The student drew a triangle ABCABC on the board, in which AB>BCAB>BC. On the side ABAB is taken point DD such that BD=ACBD = AC. Let points EE and FF be the midpoints of the segments ADAD and BCBC respectively. Then the whole picture was erased, leaving only dots EE and FF. Restore triangle ABCABC.
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