In the diagram below, angle PQR=PRQ=STR=TSR, RQ=8, SQ=2. Find PQ
Here is a hint.
Using angle equalities what type can your prove that TSR and PQR are?
As this is an AoPS question please do not post full solutions, but hints are ok.
TY! THIS HELPED A LOT
This diagram may help you solve this geometry problem.
QR = QT = 8
XT = QS = 2
XY = TL = sqrt( QT² - QL² )
TR = QX = sqrt ( XY² + QY² )
You can take it from here; it's easy.