Problem: Chords and in the circle to the right intersect at and are perpendicular to each other. If segments , and have measures , and respectively, then the length of the diameter of the circle is
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Answer Choices:
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Solution:
If and be drawn, then inscribed angles and subtend the same arc and hence right triangles and are similar. Hence and the measure of segment is . The center of the circle at the intersection of the perpendicular bisectors of chords and is units to the right of and unit above point . Hence (Radius) Diameter. The length of the diameter is .