3470.51 – A Triangle in a Circle

If AB and CD are perpendicular diameters of circle Q, and angle QPC = 60 degrees, then what is the ratio of PQ to AQ?

Solution

PQCQ=13\frac{PQ}{CQ}=\frac{1}{\sqrt{3}}, since we are looking at a 30-60 right triangle.

Since AQ = CQ, PQAQ=13=33.\frac{PQ}{AQ}=\frac{1}{\sqrt3}=\frac{\sqrt3}{3}.

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