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.

Tags

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.

Tags

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.

Tags

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

Tags

CCSS.HSG.C.A.2

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

• 90 degrees

• 270 degrees

• 45 degrees

• 180 degrees

Tags

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.

Tags

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.

Tags

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

Tags

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.

Tags

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

Tags

CCSS.HSG.C.A.2

CCSS.HSG.C.A.3