Question

Circle O is shown. Tangents X Z and Y Z intersect at point Z outside of the circle. The first arc formed is arc b, and the second arc formed is arc a.
Which equation is correct regarding the diagram of circle O?

m∠XZY = One-half(a + b)
m∠XZY = One-half(a – b)
m∠XOY = One-half(a + b)
m∠XOY = One-half(a – b)

Answer 1

m∠XZY = One-half(a – b)

Reason: The angle formed by two tangents drawn from an external point equals half the difference of the measures of the intercepted arcs (major arc − minor arc).