Circles - Central Angles, Inscribed Angles, and Inscribed Quads

What is a central angle of a circle?

• An angle whose vertex is at the center of the circle and whose sides are tangent to the circumference of the circle.

• An angle whose vertex is at the center of the circle and whose sides do not intersect with the circumference of the circle.

• An angle whose vertex is at the center of the circle and whose sides are parallel to the circumference of the circle.

• An angle whose vertex is at the center of the circle and whose sides pass through two points on the circumference of the circle.

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CCSS.HSG.C.A.2

CCSS.HSG.CO.A.1

What is an inscribed angle of a circle?

• An inscribed angle of a circle is an angle formed by two secants of the circle that intersect at a point inside the circle.

• An inscribed angle of a circle is an angle formed by two radii of the circle that intersect at the center of the circle.

• An inscribed angle of a circle is an angle formed by two tangents of the circle that intersect at a point outside the circle.

• An inscribed angle of a circle is an angle formed by two chords of the circle that have a common endpoint on the circle.

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CCSS.HSG.C.A.2

CCSS.HSG.C.A.3

What is the relationship between a central angle and an inscribed angle that intercept the same arc?

• The central angle is twice the measure of the inscribed angle.

• The central angle is half the measure of the inscribed angle.

• The central angle is equal to the measure of the inscribed angle.

• The central angle is three times the measure of the inscribed angle.

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CCSS.HSG.C.A.2

What is the measure of a central angle that intercepts a semicircle?

• 360 degrees

• 180 degrees

• 90 degrees

• 45 degrees

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CCSS.HSG.CO.A.1

CCSS.4.MD.C.5B

What is the measure of an inscribed angle that intercepts a semicircle?

• 90 degrees

• 270 degrees

• 45 degrees

• 180 degrees

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CCSS.HSG.C.A.2

What is the relationship between the measure of an inscribed angle and the measure of its intercepted arc?

• The measure of an inscribed angle is equal to the measure of its intercepted arc.

• The measure of an inscribed angle is twice the measure of its intercepted arc.

• The measure of an inscribed angle is half the measure of its intercepted arc.

• The measure of an inscribed angle is unrelated to the measure of its intercepted arc.

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CCSS.HSG.C.A.2

What is a chord of a circle?

• A chord of a circle is a line segment that connects two points outside the circle.

• A chord of a circle is a line segment that connects two points inside the circle.

• A chord of a circle is a line segment that connects the center of the circle to a point on the circle.

• A chord of a circle is a line segment that connects two points on the circle.

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CCSS.HSG.C.A.2

CCSS.HSG.CO.A.1

What is the relationship between the length of a chord and the distance from its midpoint to the center of the circle?

• The length of the chord is double the distance from its midpoint to the center of the circle

• The length of the chord is equal to the distance from its midpoint to the center of the circle

• Half the length of the chord

• The length of the chord has no relationship with the distance from its midpoint to the center of the circle

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CCSS.HSG.C.A.2

What is an inscribed quadrilateral in a circle?

• A quadrilateral with one vertex at the center of the circle.

• A quadrilateral whose four vertices all lie on the circumference of the circle.

• A quadrilateral with three sides that are tangents to the circle.

• A quadrilateral with one side that is a diameter of the circle.

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CCSS.HSG.C.A.2

CCSS.HSG.C.A.3

What is the sum of the opposite angles in an inscribed quadrilateral?

• 90

• 360

• 45

• 180

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CCSS.HSG.C.A.3