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In a triangle $$ABC$$, $$AD$$ is the altitude onto the side $$BC$$. If angle $$B$$ is acute then $$AC^2 =$$
With $$D$$ the foot of the altitude, $$AC^2 = AD^2 + DC^2$$ and $$AB^2 = AD^2 + BD^2$$. Since angle $$B$$ is acute, $$DC = BC - BD$$ (in signed form), so $$AC^2 = AB^2 - BD^2 + (BC - BD)^2 = AB^2 + BC^2 - 2BC \cdot BD$$.
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