+0

# Geometry

0
111
1

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

Jan 28, 2022

#1
+2432
0

$$\Delta OCD$$ 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