Circle Geometry and Angle Relationships

This video tutorial covers the concepts of central angles, minor and major arcs, and semi-circles in geometry. It explains how to calculate the measures of arcs and angles in a circle, including the properties of isosceles triangles formed by radii. The tutorial also includes problem-solving examples to illustrate these concepts, focusing on the relationships between arcs, angles, and chords in a circle.

What is a central angle?

• An angle with its vertex on the diameter

• An angle with its vertex on the circle

• An angle with its vertex at the center of the circle

• An angle with its vertex outside the circle

How is the measure of a minor arc determined?

• It is twice the central angle

• It is unrelated to the central angle

• It is half the central angle

• It is equal to the central angle

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CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

What is the measure of a semicircle?

• 270 degrees

• 180 degrees

• 360 degrees

• 90 degrees

What is the measure of an arc that is part of a semicircle?

• 180 degrees

• 150 degrees

• 120 degrees

• 90 degrees

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CCSS.HSG.C.A.2

If a central angle measures 100 degrees, what is the measure of the intercepted arc?

• 50 degrees

• 100 degrees

• 200 degrees

• 150 degrees

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CCSS.HSG.C.A.2

In an isosceles triangle formed by two radii and a chord, if the central angle is 100 degrees, what is the measure of each base angle?

• 30 degrees

• 40 degrees

• 50 degrees

• 60 degrees

What is the measure of a major arc if the minor arc is 140 degrees?

• 220 degrees

• 320 degrees

• 180 degrees

• 140 degrees

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CCSS.HSG.CO.C.10

In a 30-60-90 triangle, if the hypotenuse is 10, what is the length of the side opposite the 30-degree angle?

• 10√3

• 5

• 10

• 5√3

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CCSS.HSG.C.A.2

What is the length of the chord if the perpendicular from the center to the chord is 5 and the radius is 10?

• 10√3

• 10

• 5√3

• 5

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CCSS.HSG.C.A.2

How do you calculate the distance from the center of the circle to a chord?

• Using the Pythagorean theorem

• Using the properties of a 30-60-90 triangle

• Using the properties of a 45-45-90 triangle

• Using the properties of an equilateral triangle

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CCSS.HSG.C.A.2