Question

Segments AC and BD are diameters of Circle E. If arc ACD = 326 then what does arc CDB equal?

Answer 1

Since segments AC and BD are diameters of Circle E, angle ACD is a central angle that intercepts arc ACD, and angle BCD is also a central angle that intercepts arc ACD. Therefore, arc ACD is divided into two equal arcs, arc CDB and arc CAB, by the diameter CD.

Since arc ACD is 326 degrees, each of arc CDB and arc CAB is 326/2 = 163 degrees.

Therefore, arc CDB equals 163 degrees.