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?
32
6
24
12

The measure of the angle that is formed outside a circle where two secants intersect equals the positive difference of the measures of the intercepted arcs on the circle, based on the Angle of Intersecting Secants Theorem.

Given the following:

m∠ABX = 64°

Measure of intercepted arc BA = 152°

Measure of intercepted arc XA = 2(m∠ABX) [inscribed angle theorem]

Substitute

Measure of intercepted arc XA = 2(64)

Measure of intercepted arc XA = 128°

Measure of angle ACB = 1/2(arc BA - arc XA) [Angle of Intersecting Secants Theorem]

Measure of angle ACB = 1/2(152 - 128)

Measure of angle ACB = 1/2(24)

Measure of angle ACB = 12°

Thus, applying the angle of intersecting secants theorem, the measure of angle ACB is determined as: D. 12°.

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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? 32 6 24 12

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What is the Angle of Intersecting Secants Theorem?

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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?
32
6
24
12