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?
A.) 23°
B.) 32°
C.) 46°
D.) 16°

Answer 1

@Callisto

Answer 2

angle BOA = 156 (given)
angle OAB = angle OBA (base angle, isos triangle)
= (180-156)/2 (angle sum of triangle)
= 12
angle OAC = 90 (tangent perpendicular to radius)
So, angle BAC = 12+90 = 102

Angle BCA = 180 - angle CBA - angle BAC (angle sum of triangle)
= 180 - 32 - 102 =?

Answer 3

46

Answer 4

thank you, you broke it down really good

Answer 5

Yes, and welcome :)

Answer 6

This was awhile ago but this helped me so much with the same problem but different measures!

Answer 7

This is history right here