(07.01 LC) The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to th
e circle. Side BC is a secant intersecting the circle at point X: The figure shows a circle with points A and B on it and point C outside it. Side BC of triangle ABC intersects the circle at point X. A tangent to the circle at point A is drawn from point C. Arc AB measures 152 degrees, and angle CBA measures 64 degrees. What is the measure of angle ACB? A. 32° B. 6° C. 24° D. 12°
"Since measure of inscribed angle is half the measure of intercepted arc"
Measure of arc AX = 2(m∠ABX)
= 2 × 64°
= 128°
"When a tangent and secant intersect outside a circle, measure of angle between them will be half of the difference of the measures of intercepted arcs."
m∠ACB =
=
= 12°
Therefore, measure of angle ACB = 12° is the answer.