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geometry > Circles > Flashcards

Circles Flashcards

0
Q

Centre

A

Given point

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1
Q

Circle

A

Set of points in a plane at a given distance from a given point in that plane

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2
Q

Radius

A

Given distance

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3
Q

Chord

A

Segment whose end points lie on a circle

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4
Q

Secant

A

Line which contains a chord

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5
Q

Diameter

A

Chord that contains the centre of a circle

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6
Q

Tangent

A

Line in plane of the circle that intersects circle in exactly one point

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7
Q

Point of tangency

A

Point where tangent intersects circle

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8
Q

Congruent circles

A

Circles with congruent radii

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9
Q

Concentric circles

A

Circles that lie in same plane and have same centre

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10
Q

When is a polygon inscribed or a circle circumscribed? (Or vice versa)

A

When each vertex of the polygon lies on the circle

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11
Q

If a line is tangent to a circle…

A

Then the line is perpendicular to the radius drawn to the point of tangency

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12
Q

Tangents to a circle from a point are…

A

Congruent

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13
Q

If a line in the plane of a circle is perpendicular to a radius at its outer endpoint…

A

Then the line is tangent to the circle

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14
Q

Common tangent

A

Line that is tangent to each of the two coplanar circles

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15
Q

Common internal tangent

A

Intersects the segment joining the centres

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16
Q

Common external tangent

A

Does not intersect segment joining the centres

17
Q

Tangent circles

A

Coplanar circles that are tangent to the same line at the same point

18
Q

Central angle

A

Angle with its vertex at centre of the circle

19
Q

Arc

A

Unbroken part of circle

20
Q

Measure of minor arc

A

Measure of central angle

21
Q

Measure of major arc

A

360 - measure of central angle

22
Q

Measure of semicircle

A

180

23
Q

Adjacent arcs

A

Arcs that have exactly one point in common

24
Q

Arc addition postulate

A

Measure of the arc formed by two adjacent arcs is the sum of the measures of these row arcs

25
Q

In the same circle or in congruent circles two minor arcs are congruent if…

A

Their central angles are congruent

26
Q

Congruent arcs

A

Arcs in the same or congruent circles that have equal measures

27
Q

In the same or congruent circles (2 points)

A

Congruent arcs have congruent chords

Congruent chords have congruent arcs

28
Q

A diameter that is perpendicular to a chord…

A

Bisects the chord and its arc

29
Q

Inscribed angle

A

Angle whose vertex is on a circle and whose sides contain chords of the circle

30
Q

Measure of an inscribed angle is equal to…

A

Half the measure of its intercepted arc

31
Q

If two inscribed angle intercept the same arc…

A

Then the angles are congruent

32
Q

An angle inscribed in a semicircle is…

A

A right angle

33
Q

If a quadrilateral is inscribed in a circle…

A

Then its opposite angles are supplementary

34
Q

Measure of an angle formed by a chord and a tangent is equal to…

A

Half the measure of the intercepted arcs

35
Q

The measure of an angle formed by two chords that intersect inside a circle is

A

Equal to half the sum of the measures of the intercepted arcs

36
Q

The measure of an angle formed by two secants, two tangents or a secant and a tangent drawn from a point outside a circle is

A

Equal to half of the difference of the measures of the intercepted arcs

37
Q

When two chords intersect inside a circle the product of the segments of one chord equals

A

The product of the segments of the other chord

38
Q

When two secant segments are drawn to a circle from an external point,

A

The product of one secant segment and its external segment equals the product of the other secant segment and its external segment

39
Q

When a secant segment and a tangent segment are drawn to a circle from an external point

A

The product of the secant segment and its external segment is equal to the square of the tangent segment

40
Q

In same or congruent circles (chords)

A

Chords equally distant from centre are congruent

Congruent chords are equally distant from centre

geometry (7 decks)

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