Question

(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 the 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°

Answer 1

Answer:

Option (D)

Step-by-step explanation:

Measure of arc AB = 152°

"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 = $\frac{1}{2}(m\widehat {AB}-m\widehat {XA})$

             = $\frac{1}{2}(152-128)$

             = 12°

Therefore, measure of angle ACB = 12° is the answer.

Option (D) is the correct option.