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. S

Question

2 years ago

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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. S

ide 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 100 degrees, and angle CBA measures 42 degrees

What is the measure of angle ACB?

29°
8°
16°
21°

Mathematics

2 answers:

Stels [109] · Answer 1 · 2023-08-28T04:05:34+03:00

Applying the angles of intersecting secants theorem, the measure of angle ACB is: 16°.

<h3>What is the Angles of Intersecting Secants Theorem?</h3>

The angles of intersecting secants theorem states that the angle formed by two lines (secants or a tangent and a secant) that intersect outside a circle equals half the difference of the measure of the intercepted arcs.

Find m(XA) based on the inscribed angle theorem:

m(XA) = 2(m∠CBA)

Substitute

m(XA) = 2(42)

m(XA) = 84°

Based on the angles of intersecting secants theorem, we would have:

m∠ACB = 1/2[m(AB) - m(XA)]

Substitute

m∠ACB = 1/2[100 - 84]

m∠ACB = 16°

Therefore, applying the angles of intersecting secants theorem, the measure of angle ACB is: 16°.

Learn more about the angles of intersecting secants theorem on: