PQR is an acute angled triangle whose circumcenter and the orthocenter are respectively located at X and Y. The length of the side RP is greater than length of the side PQ.

PY is extended to intersect the side QR at S and, ST is drawn perpendicular to XS such that ST intersects the side PQ at T.

Determine the measure of the Angle RQP, given that Angle SYT = 70^o.

In the circumstances given, angle RQP is equal to angle SYT, and is therefore also 70°.

Moving the vertices of the triangle, in other circumstances, sometimes results in angles SYT and RQP being supplementary, rather than equal. I'm not sure what circumstances these are, but one is that in which PQ exceeds PR, and angle SYT flips from approaching 45 from above that angle to 135.

Posted by Charlie on 2008-05-04 14:00:23