CSMC 2022 Part A - Question 4, CEMC UWaterloo

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Difficulty: 5

This problem is tagged with csmc, csmc22, highschool.

(Canadian Senior Mathematics Contest 2022, Part A, Question 4, CEMC - UWaterloo)

In the diagram, $AB$ is perpendicular to $BC$, and $CD$ is perpendicular to $AD$. Also, $AC = 625$ and $AD = 600$. If $ \angle BAC = 2 \angle DAC$, what is the length of $BC$?

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