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In triangle ABC, ∠ABC = 90◦ . Point M is on side AB so that AM = MB, and CM = 4 and AC = 7. Find BC

Jun 1, 2022

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Let x = BC and y = AM = MB. By Pythagorean theorem we have $$\begin{cases}(2y)^2 + x^2 = 7^2\\y^2 + x^2 = 4^2\end{cases}$$.

Subtracting the second equation from the first gives an equation solely in y^2.

Can you take it from here?

Jun 2, 2022