In ⊙M, chords QR and ST intersect at U. What is TU if QU = 6, RU = 9, and SU = 7?

Question

In ⊙M, chords QR and ST intersect at U. What is TU if QU = 6, RU = 9, and SU = 7?

Normally I am able to do these questions easily because there is an image to go with it. However, since there is no image, I am struggling. I even tried to draw up an image, but I got the wrong answer. Can someone please help me? I would really appreciate it!

Answer 1

∠SRQ=∠STQ because they are both measured by the same arc

∠RQT=∠RST for the same reason

ΔRSU∼ΔTQU because angles are equal

Therefore SU/TU = RU/QU and you can now answer the question.

Answer 2

(QU)(UR) = (SU)(RU)