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The circle below centered at O has a radius of 5.  Find CD.

 

 Jan 28, 2022
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\(\Delta OCD\) is an isosceles triangle, with \(OC\) and \(OD\) both equal to \(5\).

 

Label the midpoint of \(CD\) as \(B\). Draw a line connecting \(O\) to \(B\). You have a 60-30-90 triangle, where the hypotenuse is \(5\). This means that \(OB\) is \(2.5\). Using the Pythagorean theorem, you find that \(CB\) is \(\sqrt{18.75}\), which means that \(CD\) is \(2\sqrt{18.75}\), which can be simplified to \(\color{purple} 5\sqrt3\).

 Jan 29, 2022
edited by BuilderBoi  Jan 29, 2022

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