A circle has a radius of 15. Let $\overline{AB}$ be a chord of the circle, such that AB = 4. What is the distance between the chord and the center of the circle?

siIviajendeukie Jun 7, 2024

#1**+1 **

Let's set the center of the circle as O.

Draw a line from O perpendicular to the chord. Let this line be OM.

\(OA = 15 \\ AM = AB / 2 = 4/2 = 2\)

Triangle AOM is right, with angle AMO being 90 degrees.

By using the pythagorean theorem, we have

\(OM = \sqrt{ OA^2 -AM^2} = \sqrt{ 15^2 - 2^2 } = \sqrt{221}\)

So sqrt221 is our answer.

Thanks! :)

NotThatSmart Jun 7, 2024

#1**+1 **

Best Answer

Let's set the center of the circle as O.

Draw a line from O perpendicular to the chord. Let this line be OM.

\(OA = 15 \\ AM = AB / 2 = 4/2 = 2\)

Triangle AOM is right, with angle AMO being 90 degrees.

By using the pythagorean theorem, we have

\(OM = \sqrt{ OA^2 -AM^2} = \sqrt{ 15^2 - 2^2 } = \sqrt{221}\)

So sqrt221 is our answer.

Thanks! :)

NotThatSmart Jun 7, 2024