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?

Guest Jun 20, 2020

#1**0 **

A circle has diameter XY = 28.

Chord AB is perpendicular to XY, has length 12, and intersects XY at point P.

By theorem: AP · PB = XP · PY

6 · 6 = x · (28 - x)

36 = 28X - x^{2}

x^{2} - 28x + 36 = 0

Now, use the quadratic formula: x = [ - -28 +/- sqrt( 28^{2} - 4·1·36 ) ] / (2·1)

x = ( 28 + sqrt(640) ) / 2 or x = ( 28 - sqrt(640) ) / 2

x = 14 + 4sqrt(10) x = 14 - 4sqrt(10)

Distance between the chord and the center of the circle: 14 - ( 14 - 4sqrt(10) ) = 4sqrt(10)

geno3141 Jun 20, 2020