Circle geometry problem involving angles, a diameter, and a tangent line.

here are the answers to your geometry questions.

The problem involves a circle with center O, where QOT is a diameter. Points Q, R, S, T, P are on the circumference. A tangent line TU touches the circle at T.

Given angles from the diagram:

• $\angle RQS = 46^\circ$
• $\angle STU = 48^\circ$ (angle between tangent TU and chord ST)
• QOT is a diameter.

We will use the following circle theorems:

• Alternate Segment Theorem: The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
• Angle in a Semicircle: The angle