in the adjacent figure, we have BX=1/2AB , BY=1/2 BC and AB=BC. show that BX=BY
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BX=1/2AB
2BX=AB.....1
BY=1/2BC
2BY=BC.....2
AB=BC.....3
from 1, 2 and 3
AB=BC=2BX=2BY
2BX=2BY
therefore, BX=BY
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