Identify the relevant theorem.

The theorem that relates an angle formed by a tangent and a chord to an angle in the alternate segment is called the Tangent-Chord Theorem (or Alternate Segment Theorem).

The Tangent-Chord Theorem states that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to the angle in the alternate segment.

In the diagram:

• RS is the tangent to the circle at point D.
• DX is a chord drawn from the point of contact D.
• $\angle XDR$ is the angle between the tangent RS and the chord DX.
• $\angle DYX$ is the angle in the alternate segment subtended by the chord DX.

According to the Tangent-Chord Theorem, the angle between the tangent RS and the chord DX ($\angle XDR$) is equal to the angle in the alternate segment ($\angle DYX$).

Therefore, we have proven: