Question

Circle O is shown. Secant A C intersects tangent C D at point C outside of the circle. Secant A C intersects circle O at point B and tangent C D intersects circle O at point D. Point E is on arc A D. Angle A C D is 57 degrees.
Aaron is standing at point C, watching his friends on a Ferris wheel. He knows that he is looking up at a 57° angle and the measure of arc BD is 80°. What is the measure of arc AED?

°

Answer 1

The angle between a tangent and a secant from an external point equals half the difference of the measures of the intercepted arcs. For ∠ACD the intercepted arcs are arc AD and arc BD, so

57 = 1/2 (m(arc AD) − m(arc BD)).

Given m(arc BD) = 80, solve:

114 = m(arc AD) − 80
m(arc AD) = 194.

Point E lies on arc AD, so m(arc AED) = 194°.