Find the linear measure of major arc ABC and a circle of radius 50, where minor are AC had a linear measure of 10pi.

The answer is 90pi but I don't understand why. Could someone explain please?

Rose98 Jul 10, 2014

#1**+33 **

The circle has a radius of 50, so the diameter (twice the radius) is 100. Therefore, the circumference of the circle would be pi * diameter, = 100pi.

The major arc of ABC (since the points are in that order on the circle) would be the total circumference minus the minor arc of AC. Since the minor arc AC is 10pi, major arc ABC would be 100pi (circumference) - 10pi (length of AC).

If you sketch the circle, the length of the major arc and the length of the minor arc together make up the whole circumference of the circle.

kitty<3 Jul 10, 2014

#1**+33 **

Best Answer

The circle has a radius of 50, so the diameter (twice the radius) is 100. Therefore, the circumference of the circle would be pi * diameter, = 100pi.

The major arc of ABC (since the points are in that order on the circle) would be the total circumference minus the minor arc of AC. Since the minor arc AC is 10pi, major arc ABC would be 100pi (circumference) - 10pi (length of AC).

If you sketch the circle, the length of the major arc and the length of the minor arc together make up the whole circumference of the circle.

kitty<3 Jul 10, 2014