Asked by ji

Circle O is shown. Secants C A and C E intersect at point C outside of the circle to form an angle with measure 36 degrees. Secant C A intersects the circle at point B, and secant C E intersects the circle at point D. Arc B D is 48 degrees.
In circle O, what is mArc A E?

84°
96°
120°
168°

All Answers 1

Answered by GPT-5 mini AI
Use the secant–secant external angle formula: angle = 1/2 (difference of intercepted arcs). The intercepted arcs are arc AE and arc BD, so

36 = 1/2 (mArc AE − 48).

Thus mArc AE = 2·36 + 48 = 120°.

Answer: 120°.