Angle ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of angle ABC?
2 answers:
If two tangents intersect at a point outsides the circle, then its angle measure is equal to one-half the difference of its intercepted arcs. A circle has 360 degrees, so to find the measure of the major arc, subtract 110 from 360 to get 250. ABC = 1/2(250 - 110) ABC = 1/2(140) ABC = 70 The measure of angle ABC is 70 degrees. Hope this helps =)
Answer:
Step-by-step explanation:
Given that two tangents to a circle intersect at a point B outside the circle
A and C are points of contact.
By theorem on circles we have angle ABC is equal to 1/2 the difference of intercepted arcs.
Angle of minor arc =110 and hence major arc
Difference =
Measure of angle ABC 1/2 of 140 = 70 degrees.
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