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Three students are trying to find the diameter of circle C. Chord XY does not pass through the center. It is to the left of the center. The length of chord XY is 72 and its midpoint is named Z. Z is 27 units to the right of point W, which is on the left perimeter of the circle midway on the arc between points X and Y on the perimeter. WZ forms a right angle with XY.

Gregory believes the diameter is equal to the length of chord XY. Maria believes chord WY can be added to create the right triangle WZY. She also thinks the hypotenuse of ΔWZY has a length equal to the radius of the circle. Jordan believes segment WZ lies on the diameter of the circle, and that if the diameter is drawn, he can make an equation relating the pieces of that diameter of the circle to the pieces of XY¯.

I know that the student with the correct approach to finding the diameter is
Jordan, but do not understand why. I think that Gregory cannot be correct because XY does not pass through the middle of the circle, so it cannot be a diameter. I am unsure about why Maria cannot be correct, but think it might be because she is confusing this with an inscribed angle, which it is not. I do not know why Jordan is correct.

I also have the answer that the diameter of the circle is 75 units, but have no idea how this was calculated. Can you help?

Sagot :

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