Thread: cyclic quadrilateral

PQRS is a cyclic quadrilateral where angle PQR and angle QRS are obtuse and have the same value . IF PQ=9 , QR=6 , and RS=4 , prove that if T is the point of intersection of the diagonals , then the circle that passes through R,S and T touches QR at R .

I think it's something wrong with this problem.
If then

Then and the quadrilater is an isosceles trapezoid. Then .

But .

If this inscribed quadrilateral has 2 equal obtuse angles, it is most certainly an isosceles trapezoid / trapezium, and so PQ and RS is supposed to have the same length.