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December 5th, 2017, 11:09 PM   #1
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geometry proof triangle

It's an equilateral triangle named "ABC"
The center point of the triangle is named "O"

The circle that crosses "A" point and "O" crosses "AB" in "M" point and "AC" in "N" point . Prove that AN = BM.

Last edited by skipjack; December 6th, 2017 at 06:43 PM.
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December 6th, 2017, 02:24 PM   #2
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Equilateral triangle is congruent to itself by flipping along OA line.
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December 6th, 2017, 07:56 PM   #3
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OA = OB (given)
ON = OM (because $\small\angle$NAO = $\small\angle$MAO = 30$^\circ$)
$\small\angle$AON = $\small\angle$BOM (because $\small\angle$MON = $\small\angle$BOA = 120$^\circ$)
Hence triangles ANO, BMO are congruent (SAS), which implies AN = BM.
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