SOLUTION: Suppose that triangle ABC has a 30-degree angle at A and a 60-degree angle at B. Let O be the midpoint of AB. Draw the circle centered at O that goes through A. Explain why this ci

Question 1154879: Suppose that triangle ABC has a 30-degree angle at A and a 60-degree angle at B. Let O be the midpoint of AB. Draw the circle centered at O that goes through A. Explain why this circle also goes through B and C. Angle BOC is called a central angle of the circle because its vertex is at the center. The minor arc BC is called a 60-degree arc because it subtends a 60-degree angle at the center. What is the angular size of minor arc AC? of major arc AC? How does the actual length of minor arc AC compare to the length of minor arc BC?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A circle with center at the midpoint of the hypotenuse of a right triangle, and diameter equal to the hypotenuse, circumscribes the triangle, so all the vertices of the triangle are points on the circle.

Since AB is a diameter (dividing the circle into two 180-degree arcs) and arc BC is 60 degrees, minor arc AC is 120 degrees. Then of course major arc AC is 360-120=240 degrees.

The angle measure of minor arc AC is twice the angle measure of minor arc BC; since they are arcs of the same circle, the actual length of minor arc AC is twice the length of minor arc BC.

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