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Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse ACAC. If AC=19AC=19 and DC=4,DC=4, what is the length of \overline{BC}BC in simplest radical form? (Note: the figure is not drawn to scale.)

 Mar 3, 2021
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Lets call BD x. using pythagorean theorum, we have:

 

16+x^2+225+x^2=361

241+2x^2=361

x^2=60

x=$\boxed{2\sqrt{15}}$

 Mar 3, 2021

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