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Points A, B, and C are located on a circle, and chords exist between all three points. If the measure of ∠BAC is 88°, what is the measure of BC?

OA. 88°
OB. 92°
Oc. 176°
OD 184°

1 Answer

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Final answer:

The measure of chord BC, given that the measure of ∠BAC is 88°, is 176° because an inscribed angle is half the measure of its intercepted arc.

Step-by-step explanation:

The question asks us to determine the measure of chord BC in a circle where points A, B, and C form a triangle with a given angle measure for ∠BAC. It is important in this solution to understand a property of circles: An angle that is inscribed in a circle is half the measure of its intercepted arc. Since ∠BAC is given as 88°, the arc BC that it intercepts will be 176° because the arc measure is twice the angle measure.

To find the measure of BC, we need to use the fact that the measure of an angle subtended by a chord is equal to half the measure of the arc it cuts off.

Given that ∠BAC is 88°, we can use the formula: ∠BAC = 0.5 * measure of arc BC. Solving for the measure of arc BC, we get: measure of arc BC = 2 * ∠BAC = 2 * 88° = 176°.

Therefore, the measure of BC is 176°.

The correct option is Oc. 176°

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