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Gọi S là diện tích tam giác, thì:
$S=\frac{abc}{4R}=2R^2\sin A\sin B\sin C$
Ta có:
$h_ah_bh_c=\frac{2S}{a}.\frac{2S}{a}.\frac{2S}{c}$
$=\frac{8S^3}{abc}$
$=\frac{\displaystyle8.\frac{abc}{4R}(2R^2\sin A\sin B\sin C)^2}{abc}=8R^3\sin^2A\sin^2B\sin^2C$
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