Question

In circle Q, ∠RQS ≅ ∠SQT.

Circle Q is shown. Line segments Q R, Q S, Q T, Q U, and Q U are radii. Lines are drawn to connect the point on the circle to create secants U V, V R, R S, S T, and T U.

Which statement must be true?

Answer 1

∠RQS ≅ ∠SQT are equal central angles, so they intercept equal arcs. Therefore arc RS = arc ST. Hence the chords RS and ST are congruent (RS ≅ ST).