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(2 questions!) In circle O, which segment is a tangent?

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1 In circle O, which segment is a tangent?

A- OH->

B- SD->

C- OC->

D- RC->

-------------------------------------------------------------------------------------------- What is the measure of Arc ADB?

Question  options:

72°

18°

288°

108°

Jun 3, 2018

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1) A tangent segment, by definition, is an exterior segment of a circle that intersects a circle at one and only one point (known as the point of tangency).

$$\overline{OH}$$ is in the interior region of a circle, so it cannot be a tangent segment. Radii are never tangent segments.

$$\overline{SD}$$ fits the definition of a tangent segment and is, therefore, a tangent segment.

$$\overline{OC}$$ is in the interior region of a circle, so it cannot be a tangent segment.

$$\overline{RC}$$ is in the interior region of a circle, so it cannot be a tangent segment.

2) $$m\angle ADB=\frac{1}{2}m\widehat{AB}$$ by the Inscribed Angle Theorem. This means that $$m\widehat{AB}=72^{\circ}$$. Wait! We are not done, though. The question asks for the measure of the major arc, the one that has a measure of more than 180°. I know this because there are 3 letters in the arc's name.

Therefore, $$m\widehat{ADB}=360-72=288^{\circ}$$

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Jun 3, 2018