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2024 SSMO Speed Round Problems/Problem 5

Revision as of 15:41, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>\triangle ABC</math> and <math>\triangle ADC</math> be right triangles, such that <math>\angle ABC = \angle ADC = 90^\circ</math>. Given that <math>\ang...")
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Problem

Let $\triangle ABC$ and $\triangle ADC$ be right triangles, such that $\angle ABC = \angle ADC = 90^\circ$. Given that $\angle ACB = 30^\circ$ and $BC = 3\sqrt{3}$, find the maximum possible length of $BD$.

Solution

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