In circle O, diameter AB̅, chord BC̅, and radius OC̅ are drawn, and the m of arc BC : m of arc BC = 5 : 3

Question

In circle O, diameter AB̅, chord BC̅, and radius OC̅ are drawn, and the m of arc BC : m of arc BC = 5 : 3.

What is the mABC?

Answer 1

Since arc AB is 1/2 the circle, i.e. 180 degrees,

arc BC = 67.5 and arc AC = 112.5

The angle ABC = 1/2 * 112.5 = 56.25

Arc BC:arc AC = 5:3 means arc AC/arc BC = 3/5

Add 1 to each side: (arc AC + arc BC)/arc BC = 8/5

180/arc BC = 8/5 => arc BC = 112.5 and then arc AC = 67.5.