Chapter 10.1 - 10.3 Circles

Question 1

Exterior of a circle

Answer 1

Points outside of a circle.

Question 2

Chord

Answer 2

A segment whose endpoints are on the circle.

Question 3

Diameter

Answer 3

A chord that passes through the center of a circle.

Question 4

Radius

Answer 4

A segment whose endpoints consist of the center of the circle and a point on the circle.

Question 5

Tangent

Answer 5

If a line intersects a circle at exactly one point, then the line is a tangent of the circle.

Question 6

Secant

Answer 6

If a line intersects a circle at two points, then the line is a secant of the circle.

Question 7

Common tangent

Answer 7

A line that is tangent to two circles.

Question 8

Common external tangent

Answer 8

A common tangent that does not intersects the segment that joins the centers of the circle.

Question 9

Interior of a circle

Answer 9

Points inside of a circle.

Question 9

Common internal tangent

Answer 9

A common tangent that intersects the segment that joins the centers of the circle.

Question 11

Two circles can intersect in 4 different ways:

Answer 11

1) two circles can have no points of intersection.
2) two circle can have exactly one point of intersection ( circles are tangent to each other ).
3) two circles can have exactly two points of intersection.
4) two circles can have infinitely many points of intersection.

Question 12

Concentric circles

Answer 12

Circles that have the same center.

Question 13

Congruent circles

Answer 13

Circles with congruent radii or diameters.

Question 14

Theorem 10.1

Answer 14

If a line is tangent to a circle, then it is perpendicular to the radius drown to the point of tangency.

Question 15

Theorem 10.2

Answer 15

In a plane, if a line is perpendicular to a radius of a circle, at its endpoints on the circle, then the line is tangent to a circle.

Question 16

Theorem 10.3

Answer 16

If two segments from the same exterior point are tangent to a circle, then they are congruent.

Question 17

Inscribed circle

Answer 17

A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.

Question 18

Circumscribed circle

Answer 18

A circle is circumscribed about a polygon if each vertex of a polygon lies on the circle.

Question 19

Circle

Answer 19

Set of all points in a plane that are equidistant from a given point called the center.

Question 20

Central Angle

Answer 20

An angle whose vertex is the center of the circle.

Question 21

Minor arc

Answer 21

Consists of the endpoints of the central angle and all points on the circle that are in the interior of the central angle.

Question 22

Measure of a minor arc

Answer 22

The measure of the central angle.

Question 23

Semicircle

Answer 23

An arc whose endpoints arc the endpoints of the diameter.

Question 24

Major arc

Answer 24

Consists of the endpoints of the central angle and all points on the circle that lie in the exterior of the central angle.

Question 25

Adjacent arcs

Answer 25

Two arcs of the same circle are adjacent if they intersect at exactly one point.

Question 26

Postulate 21 Arc Addition Postulate

Answer 26

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Question 27

Congruent arcs

Answer 27

In the same circle or congruent circles, two arcs are congruent if they have the same measure.

Question 28

Theorem 10.4

Answer 28

In the same circle or in congruent circles, two arcs are congruent iff their central angles are congruent.