Question

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X.
What is the measure of angle ACB?

Answer 1

Can you find arc XA?

Answer 2

arc XA is twice its inscribed angle XBA.
So what is arc XA?

Answer 3

Is arc XA 112?

Answer 4

yes

Answer 5

Would that mean that angle C is 68 degrees after using the exterior angle theorem?

Answer 6

no. I don't remember what it's called but there's another theorem about secants intersecting exterior to the circle. Basically you subtract the intercepting arcs and divide by 2.

Angle C = (arc AB - arc XA)/2 = (176 - 112)/2 = 32

Answer 7

Ooohhhh, thank you so much!!

Answer 8

yw