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A circle has a radius of 10.  A chord of distance 16 is drawn inside the circle.  What is the distance from the center of the circle to the chord?  I don't understand.

 Jul 4, 2020
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Let O be the center of the circle.

Let CD be the chord of length 16

Let AOB be the diameter of the circle that is the perpendicular bisector of the chord; A is on minor arc(CD)

     and D is on major arc(CD).

Let the point of intersection of AOB and CD be point X.

 

Being a radius, OD = 10.

XD = 8.

Triangle(OXD) is a right triangle.     OX2 + XD2  =  OD2  

                                                           OX2 + 82  =  102 

                                                           OX2 + 64  =  100

                                                                   OX2  =  36

                                                                     OX  =  6

 

OX is the distance from the center to the chord.

 Jul 4, 2020

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