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Math > Chapter 10 > Flashcards

Chapter 10 Flashcards

0
Q

Chord

A

A segment whose endpoints are on a circle

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1
Q

Cirle

A

Set of. All points in a plane that are equidistant from a certain point called the center. The points inside the circle form it’s interior. The points outside the circle form it’s exterior.

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2
Q

Diameter

A

A chord that passes through the center

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3
Q

Radious

A

A segment that has a center as one endpoint and a point on the circle as another

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4
Q

Tangent

A

A line that intersects a circle at exactly one point

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5
Q

Point of tangency

A

The point at which the tangent intersects

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6
Q

Secant

A

A line that intersects a circle at two points

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7
Q

Common tangent

A

A line that is tangent to two circles

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8
Q

Common external tangent

A

A common tangent that does not intersect the segment that joins the centers of the circles

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9
Q

Common internal tangent

A

A common tangent that intersects the segment that joins the centers of the circles

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10
Q

Concentric circles

A

Circles that have the same center

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11
Q

Congruent circles

A

Circles with congruent radii or diameters

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12
Q

Thm 10.1

A

If a line is tangent to a circle then it is perpendicular to the radio us drawn to the point of tangency

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13
Q

Thm 10.2

A

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

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14
Q

Thm 10.3

A

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

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15
Q

Inscribed circle

A

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

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16
Q

Circumscribed circle

A

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

17
Q

Central angle

A

An angle whose vertex is the center of a circle and whose sides pass through a pair of points on the circle

18
Q

Minor arcs

A

A shorter ace joining two points together on a circumference

19
Q

Measure of a minor arc

A

The smaller arc when a circle is divided unequally

20
Q

Semi circle

A

A circle cut on the diameter

21
Q

Major arc

A

A longer arc joining two points together on a circumference

22
Q

Measure of a major arc

A

The bigger arc when a circle is divided unequally

23
Q

Adjacent arc

A

Two arcs on a circle that share exactly one endpoint

24
Q

Arc addition postulate

A

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

25
Q

Congruent arcs

A

Arcs with the same measure on the same congruent circles

26
Q

Thm 10.4

A

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

27
Q

Thm 10.13

A

If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is half the measure of the intercepted arc

28
Q

Thm 10.14

A

If two chords intersect in the interior of a circle, then the measure of each angle is half the sum of the measures of the arcs intercepted by the angle, and it’s verticals angle

29
Q

Thm 10.15

A

If a tangent and a secant, two tangents, or two secants, intersect in the exterior of a circle then the measure of the angle formed is half the difference of the measures of the intercepted arcs

30
Q

Thm 10.5

A

In the same circle or in congruent circles, two minor arcs are congruent iff their corresponding chords are congruent

31
Q

Thm 10.6

A

If a diameter of a circle is perpendicular to a chord, then the diameter bisects it’s chord at the arc

32
Q

Thm 10.7

A

If a chord is perp to a bisector of another chord, then it is the diameter

33
Q

Thm 10.8

A

In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center

34
Q

Inscribed angle of a circle

A

An angle who’s vertex is on the circle and sides are part of the circle

35
Q

Intercepted arc

A

Te arc that lies in the interior of an inscribed angle

36
Q

Thm 10.9

A

If an angle is inscribed in a circle then it’s measure is half the measure of it’s intercepted arc

37
Q

Thm 10.10

A

If two inscribed angles of a circle intercept the same arc, then the angles are congruent

38
Q

Thm 10.11

A

An angle that is inscribed in a circle is a right angle iff it’s corresponding arc is a semicircle

39
Q

Thm 10.12

A

A quadrilateral can be inscribed in a circle iff it’s opposite angles are supplementary

Math (18 decks)

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