Question

Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.
Which equation is correct regarding the measure of ∠1?

m∠1 = One-half(a – c)
m∠1 = One-half(a + c)
m∠1 = One-half(b – d)
m∠1 = One-half(b + d)

Answer 1

Use the external-secant theorem: an angle formed outside a circle by two secants equals one-half the difference of the measures of the intercepted arcs. The intercepted arcs here are b and d, so

m∠1 = 1/2(b − d)

(or equivalently 1/2|b − d| if you want the positive difference).