In the diagram of circle o, what is the measure of ∠abc?
Asked by wiki @ in Mathematics viewed by 340 People
27°
54°
108°
120°
Asked by wiki @ in Mathematics viewed by 340 People
27°
54°
108°
120°
Answered by wiki @
Given:
Given that a circle O with two tangents BA and BC.
The major arc AC is 234°
The minor arc AC is 126°
We need to determine the measure of ∠ABC
Measure of ∠ABC:
We know the property that, "if a tangent and a secant, two tangents or two secants intersect in the interior of the circle, then the measure of angle formed is one half the difference of the measures of the intercepted arcs."
Hence, applying the above property, we have;
Substituting the values, we get;
Thus, the measure of ∠ABC is 54°
Hence, Option b is the correct answer.
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