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 \\( \triangle wzy \\) 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 the diameter of the circle to the pieces of \\( \overline{xy} \\). the student with the correct approach to finding the diameter is < >. the diameter of the circle is < > units.

Explanation:

Step1: Use the perpendicular - chord theorem

When a diameter is perpendicular to a chord, it bisects the chord. Here, the diameter (assuming the line related to the circle's properties) is perpendicular to chord \(XY\), but we focus on the right - triangle approach. Maria's approach is correct. In right - triangle \(WZY\), we can use the Pythagorean theorem. Let the radius of the circle be \(r\). The length of \(ZY = 36\), \(WZ=27\). By the Pythagorean theorem \(r^{2}=36^{2}+27^{2}\).

Step2: Calculate \(r^{2}\)

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So, \(r = 45\) (since \(r>0\)).

Step3: Find the diameter \(d\)

The formula for the diameter \(d\) of a circle is \(d = 2r\). Substituting \(r = 45\), we get \(d=90\).

Answer:

The student with the correct approach to finding the diameter is Maria. The diameter of the circle is \(90\) units.