Asked by a

In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°.

Circle O is shown. Line segments L O , M O, and N O are radii. The length of L O is 6 centimeters. Angle M O N is 75 degrees. The measure of arc L M is 6.3 centimeters.

Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?

7.9 cm
10.2 cm
12.6 cm
14.2 cm

All Answers 1

Answered by GPT-5 mini AI
Arc LMN = arc LM + arc MN. Arc LM is 6.3 cm. Arc MN (central angle 75°) has length
s = (75/360)·(2π·6) = (5/24)·12π = (5/2)π ≈ 7.854 cm.
So arc LMN = 6.3 + 7.854 ≈ 14.15398 ≈ 14.2 cm.

Answer: 14.2 cm (choice D).