P, Q and R are three points located on a circle L with diameter 4 and satisfying PQ = QR. Point S is located inside L in such a manner that QR = RS = SQ. The line passing through P and S intersects L at the point T.

Determine the length of ST.

If we assume there is one answer, regardless of the actual measure of PQ ( = RS), then we can allow arc PQ and arc QR to be 60 degrees each. In that case, line PST is a diameter of L, with S at the center.

ST is then the radius, of length 2.

Geometer's Sketchpad verifies that as one changes the arclength PQ, and the matching arclength QR, the length of ST remains the same.

 

Posted by Charlie on 2008-01-25 15:38:54