A circle has a radius of 14. Let AB be a chord of the circle, such that AB = 12. What is the distance between the chord and the center of the circle?

Otterstar May 21, 2020

#1**+2 **

The distance from the chord to the center of the circle is the distance from the center of the chord to the center of the circle.

Drawing a triangle from the center of the circle to the center of the chord (x), then from the center of the chord to the end of the chord (6), and finally from the end ot the chord to the center of the circle (14), we have a right triangle with the Pyhagorian Theorem: x^{2} + 6^{2} = 14^{2}.

Solving this, we get x^{2} = 160 and x = sqrt(160).

geno3141 May 21, 2020

#1**+2 **

Best Answer

The distance from the chord to the center of the circle is the distance from the center of the chord to the center of the circle.

Drawing a triangle from the center of the circle to the center of the chord (x), then from the center of the chord to the end of the chord (6), and finally from the end ot the chord to the center of the circle (14), we have a right triangle with the Pyhagorian Theorem: x^{2} + 6^{2} = 14^{2}.

Solving this, we get x^{2} = 160 and x = sqrt(160).

geno3141 May 21, 2020