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Question
In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC
intersects FE at Q. Prove that AQ = QP.
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Solution
In ΔABC
E and F are midpoints of AB and AC
∴ EF || FE, `1/2` BC =FE [ ∴ By mid-point theorem]
In ΔABP
F is the midpoint of AB and FQ || BP [ ∵ EF || BC ]
∴ Q is the midpoint of AP [By converse of midpoint theorem]
Hence, AQ = QP
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