Question

select the correct answer from each drop - down menu.
three students are trying to find the diameter of circle c.
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 (overline{xy}).
the student with the correct approach to finding the diameter is (\boldsymbol{\text{jordan}}). the diameter of the circle is (\boldsymbol{\text{dropdown with 45, 72, 75}}) units.

Explanation:

Step1: Identify chord segments

Chord XY is split by point Z into segments XZ=36 and ZY=36. Chord WZ is 27, and Z lies on a diameter (let the diameter be AB passing through Z, so AZ = r + d, BZ = r - d if CZ = d, but using power of a point: for point Z inside circle, product of segments of one chord equals product of segments of another chord.

Step2: Apply power of a point theorem

Power of Z: \(XZ \times ZY = WZ \times ZD\) where ZD is the other segment of the diameter through Z. Let ZD = x, so \(36 \times 36 = 27 \times x\).

Step3: Calculate x

\(x = \frac{36 \times 36}{27} = \frac{1296}{27} = 48\).

Step4: Find diameter

Diameter = WZ + ZD = 27 + 48 = 75.

Answer:

The student with the correct approach is Jordan; The diameter of the circle is 75 units.