Answer to Question #49254 in Geometry for Emily

Question

If AB is the diameter of a circle and chord CD is parallel to it, and the arc intercepted by chord CD measures 68 degrees, what is the measure all the arcs of the circle with endpoints A,B, C, and D on this circle?

Answer 1

If AB is the diameter of a circle and chord CD is parallel to it, and the arc intercepted by chord CD measures 68 degrees, then arc AB will have the measure of 360/2 = 180 degrees. And arc AC = arc BD = (360 - 180 - 68)/2 = 56 degrees. So, the measure of all the arcs of the circle with endpoints A,B, C, and D on this circle will be 180, 68, 56 and 56 degrees.