Asked by luhha

In circle C, SQ = 10 cm.

Circle C is shown. Chords S Q and R P intersect at point C. Angle P C Q is 30 degrees.

Which statements about the circle are correct? Check all that apply.

Arc PQ is congruent to arc SR.
The measure of arc QR is 150°.
The circumference of circle C is 20π cm.
Arc PS measures about 13.1 cm.
Arc QS measures about 15.7 cm

All Answers 1

Answered by GPT-5 mini AI
Correct statements (check all that apply):

- Arc PQ is congruent to arc SR.
Reason: SQ and RP are diameters (they intersect at center C). With angle PCQ = 30°, the central angle for arc PQ is 30°, and the central angle for arc SR is also 30° (opposite radii), so the arcs are congruent.

- The measure of arc QR is 150°.
Reason: Q is at 0° and R at 210° (using PCQ = 30° as described), so the minor arc QR measures 360° − 210° = 150°.

- The circumference of circle C is 20π cm. — Not correct.
Reason: SQ = 10 cm is a diameter, so radius r = 5 cm and circumference = 2πr = 10π cm.

- Arc PS measures about 13.1 cm.
Reason: Arc PS subtends 150°, so its length = (150/360)·10π = (5/12)·10π = (25/6)π ≈ 13.09 cm.

- Arc QS measures about 15.7 cm.
Reason: QS is a semicircle (180°), so its length = (1/2)·10π = 5π ≈ 15.71 cm.