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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.

 Apr 10, 2019
 #1
avatar+105454 
+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)

 

 

cool  cool cool

 Apr 10, 2019
 #2
avatar+1015 
-4

So yeah as C-Phill said 2sqrt(5)

Nickolas  Apr 10, 2019

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