PQR is a right angled triangle with hypotenuse PQ while PR = √2 and QR = 1. S is the midpoint of PQ and T is the midpoint of PR. The line segments QT and RS intersect at the point U.

Determine Angle QUR.

TUS and QUR are similar triangles.
So, TS=1/2(as T and S are midpoints),TR=1/√2
QU=2*TU and RU=2*SU
RSē=TRē+TSē=1/2+1/4
=> RS=√3/2 => RU = 1/√3
Similarly QT=√1.5 = QU = √(2/3)
Consider triangle RUQ
cos(QUR)=(1/3+2/3-1)/(2*1/√3*√(2/3)) = 0
=> Angle QUR = 90

Posted by Praneeth on 2007-12-11 06:28:09