A circle has a radius of three inches. The distance from the center of the circle to chord CD is two inches. How many inches long is chord CD?Express your answer in simplest radical form.

SydSu22 Apr 10, 2019

#1**+2 **

The "distance" can be represented by a segment drawn from the center that is a perpendicular bisector of the chord......call the point of intersection, E......call the center of the circle O....so OE = 2

So...we have a right triangle with the radius = the hypotenuse = 3....segment OE being a leg = 2 and ED being the other leg

So 1/2 of the chord length = sqrt [ radius^2 - 2^2 ] = sqrt [ 3^2 - 2^2] = sqrt [ 9 - 4 ] = sqrt (5)

And chord CD is twice this length = 2sqrt (5)

CPhill Apr 10, 2019