Question

in circle t, $\angle ptq \cong \angle rts$. what is the length of $\overline{pq}$? \bigcirc 3 units \bigcirc 4 units \bigcirc 6 units \bigcirc 7 units

Explanation:

Step1: Identify congruent central angles

We know $\angle PTQ \cong \angle RTS$. In a circle, congruent central angles correspond to congruent chords.

Step2: Match congruent chords

Chord $\overline{PQ}$ corresponds to $\angle PTQ$, and chord $\overline{SR}$ corresponds to $\angle RTS$. Since $\angle PTQ \cong \angle RTS$, $\overline{PQ} \cong \overline{SR}$. The length of $\overline{SR}$ is 4 units.

Answer:

4 units