This is simlpy an AAA problem.
Inscribed angles intersecting the same arc are congruent.
Vertical angles are congruent.
Fill in the blanks...
Given: Line PS and Line QT are chords intersecting at R.
Prove: Triangle QRP is similar to Triangle SRT
Statements & Reasons
Line PS and Line QT are chords intersecting at R : Given
Angle QPS is congruent to Angle STQ & Angle PQT is congruent to Angle TSP : ____________________
Triangle QRP is similar to Triangle SRT : ___________________