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 20080504 14:00:23 