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2 years ago

∠ABC is formed by two tangents intersecting outside of a circle. If minor arc AC = 110°, what is the measure of ∠ABC?

Mathematics

2 answers:

tatyana61 [14]2 years ago

6 0

The answer to this problem is 70. Hope I helped :)

Mariulka [41]2 years ago

5 0

Answer:

∠ABC = 70°

Step-by-step explanation:

As shown in the figure attached AB and BC are two tangents drawn on a circle touching at A and C.

Measure of minor arc = 110°

And we have to find the measurement of ∠ABC.

Since measure of minor arc AC = 110°

and m(minor arc AC) + m(major arc AC) = 360°

110° + major arc AC = 360°

major arc AC = 360 - 110 = 250°

and angle formed outside the circle by two tangents formed at B = 1/2(difference of intercepted arcs)

= $\frac{1}{2}(major arc - minor arc)=\frac{1}{2}(250-110)=\frac{1}{2}(140)=70$

Therefore answer is ∠ABC = 70°

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