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Geometry > Chapter 10 > Flashcards

Chapter 10 Flashcards

1
Q

What is a tangent?

A

a line that intersects a circle at exactly one point

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2
Q

Theorem 12-1:

if a line is tangent to a circle then the line is…

A

perpendicular to the radius drawn to the point of tangency

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3
Q

Theorem 12-2:

if a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle…

A

then the line is tangent to the circle

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4
Q

Theorem 12-3:

The two segments tangent to the outside of a circle are…

A

congruent

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5
Q

What is a chord?

A

A segment whose endpoints are on a circle

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6
Q

What is a diameter?

A

A chord that goes through the center of a circle

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7
Q

What is an arc?

A

pieces of a circle

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8
Q

what is a minor arc?

A

an arc that is less than 180 degrees

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9
Q

what is a major arc?

A

an arc that is more than 180 degrees

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10
Q

what is a semicircle?

A

an arc that is exactly 180 degrees

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11
Q

what is a central angle?

A

an angle made up of two segments whose vertex is the center of the circle

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12
Q

Theorem 12-4:

within a circle or in congruent circles… (three things)

A
  1. Congruent central angles have congruent chords
  2. Congruent chords have congruent arcs
  3. Congruent arcs have congruent central angles
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13
Q

Theorem 12-5:

within a circle or congruent circles… (two things)

A
  1. Chords equidistant from the center are congruent

2. Congruent chords are equidistant from the center

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14
Q

Theorem 12-6:

In a circle, a diameter that is perpendicular to a chord…

A

bisects the chord and its arcs

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15
Q

Theorem 12-7:

In a circle, a diameter that bisects a chord (that is not a diameter)…

A

is perpendicular to the chord

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16
Q

Theorem 12-8:

In a circle, the perpendicular bisector of a chord contains…

A

the center of the circle

17
Q

What is an inscribed angle?

A

an angle whose sides are chords and whose vertex is ON the circle

18
Q

Theorem 12-9:

the measure of an inscribed angle is…

A

half the measure of its intercepted arc

19
Q

Two inscribed angles that intercept the same arc are…

A

congruent

20
Q

An angle inscribed in a semicircle is always…

A

a right angle

21
Q

The opposite angles of a quadrilateral inscribed in a circle are…

A

supplementary

22
Q

Theorem 12-10:

The measure of an angle formed by a tangent and a chord is…

A

half the measure of an intercepted arc

23
Q

What is a secant?

A

a chord that extends outside the circle, and has two endpoints lying on the circle

24
Q

Theorem 12-11:

the measure of an angle formed by two lines that… (two things, one is inside, other is outside)

A
  1. intersect INSIDE a circle is half the SUM of the measures of the intercepted arcs (but not the center)
  2. intersect OUTSIDE the circle is half the DIFFERENCE of the measures of the intercepted arcs
25
Q

Trick for 2 tangent circles

A

angle + arc = 180

26
Q

Theroem 12-12 (Part 1):

how do you find part of the length of two chords intersecting inside a circle?

A

the product of the pieces of one chord is equal to the product of the pieces of the other chord

27
Q

Theorem 12-12 (Part 2):

two secants intersect outside a circle

A

(whole secant) (outside piece) = (whole secant) (outside piece)

28
Q

Theorem 12-12 (Part 3):

a tangent and a secant intersect outside a circle

A

(whole secant) (outside piece) = (tangent)^2

29
Q

Theorem 12-13:

what is the equation of a circle?

A

(x-h)^2 + (y-k)^2 = r^2

where r is the radius and (h,k) is the center

this is known as standard form

30
Q

How do you complete the square and get a circle in Standard Form?

A
  1. Gather the x terms and y terms so they are next to each other in the equation. Get the constant on the other side.
  2. Look at the coefficients of the x term and the y term. Divide the coefficients by 2 and square them. Add those numbers to BOTH sides
  3. Factor the x-trinomial and the y-trinomial. Both must factor into the same parenthesis twice. ex: (x-4)^2
    The circle is not un the correct form.
31
Q

If there is a plus (+) in the equation it is a…

A

circle!

32
Q

if there is a minus (-) the the equation it is a…

A

ellipse or hyperbola! don’t fall for those!

33
Q

Theorem 10-9: Circumference of a Circle

A

the circumference of a circle is π times the diameter

C= πd OR 2πr

34
Q

What is an Arc Length?

A

a fraction of the circle’s circumference

35
Q

Theorem 10-10: Arc Length

A

the length of an arc of a circle is the product of the ratio of the measure of the arc and the circumference of the circle

length = n
—— x 2πr
360

36
Q

what is “Exact Area”

A

the answer in terms of pi (π)

37
Q

Theorem 10-11: Area of a Circle

A

A = πr^2

38
Q

Theorem 10-12: Area of a Sector of a Circle

A

Sector Area = n
—— x πr^2
360

Geometry (7 decks)

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