SOLUTION: The number of points on a circle that are equidistant from the endpoints of a given diameter is: (A) 1 (B) 2 (C) 3 D) 4 (E) 5

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Question 264870: The number of points on a circle that are equidistant from the endpoints of a
given diameter is:
(A) 1 (B) 2 (C) 3 D) 4 (E) 5
Found 2 solutions by Theo, JBarnum:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
I think 2.

If the end points of the diameter are A and B, then the points equidistant from them would be the end points of a diameter perpendicular to the original diameter.

If the end points of this diameter were C and D, then C is equidistant from A and B, and D is equidistant from A and B.

All points, A,B,C,D, lie on the circumference of the circle.

The diameters of this circle would look like this: 



                                     C
                                     
                                     x

                                     x

                      A  x  x  x  x  x  x  x  x  x  B

                                     x

                                     x

                                     D



Answer by JBarnum(2146)   (Show Source): You can put this solution on YOUR website!
the answer is 2 because if u draw a circle then draw a line through the middle creating the diameter, the 2 intersecting points on the circle are "x" and "y"
so line(xy)=diameter. if u plot another point on the circle "j", line(xj) or line(jy) will not be the same distance as line(xy). so only 2 points are possible to have the same distance as the diameter.
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