circle facts pt.1 Flashcards
a line segment from the center of a circle to ANY point on the circle
radius
line segment whose endpoints are both points on the circle
chord (yay)
a chord passing through the CENTER of the circle
diameter
a line intersecting the circle in exactly one point (point of tangency), does not touch circle except for this one particular spot
tangent
a line intersecting or passing through the circle in 2 different distinct points
secant
an angle whose vertex is the center (!) of the circle and whose rays are radii of the circle
central angle
a part of the circle; can be intercepted by angles, chords, secants, and tangents
arc
an angle whose vertex is on the circle and whose rays are chords (!) of the circle
inscribed angle
an arc forming half a circle
semicircle!
an arc measuring LESS than a semicircle (2 LETTERS)
minor arc
an arc measuring MORE than a semicircle (3 LETTERS)
major arc
circles with the same center but not necessarily the same radius
concentric circles
where can a circle be inscribed?
a polygon with each side of the polygon tangent to the circle
(x-h)2 + (y-k)2 = r2
center radius form
ax2 + bx2 + cx + dy + e = 0
standard form
Circle Fact 1
A central angle is = to its intercepted arc (in degrees)
Circle Fact 2
An inscribed angle is equal to half its intercepted arc in degrees
when given a question listing 2 coordinates on a plane asking for the area of a sector
match up right triangle, find value of x via inverse of tangent and proceed with area sector formula
Limit argument (dissection)
the smaller the angle values are of each sector the circle is divided into, the more it resembles a parallelogram
Semi circle SA
1/2 pi radius squared
Quarter Circle SA
1/4 pi radius squared
any sector SA
x/360 pi radius squared
Arc length
n/360 pi diameter or n/360 2 pi radius
construction for equilateral triangle
1) diameter & plot
2) draw vertical curve after using compass to measure radius
3) connect plots
construction for hexagon
1) diameter & plot
2) draw vertical curve after using compass to measure radius
3) connect plots
4) do for both sides
construction of a square
1) diameter and plot
2) perp bisect
3) connect plots
construction of an octagon
1) diameter and plot
2) perp bisect (4x)
4) connect plots
radian measure
radius to degrees - 180 over pi
degrees to radius- pi over 180
(x-h)2 + (y-k)2 = r2
circle radius form, convert to standard form via perfect square
ax2 + by2 +cx +dy + e = 0
standard form, combine like terms
circumference formula
pi(d) or 2pi(r)
limit argument for area & circumference
the smaller the angle measure at which each sector is dissected, the more it resembles a parallelogram
1/2 (2 pi r
Radius is height
Base x2 = circumference
1/2 (2pir) (r)
base = 1/2 (2 pi r), simplifies to pi r
plus the radius is pi r2, which is the area of a rectangle
Circle Fact 3
An angle formed by a chord and a tangent is equal to half its intercepted arc
Circle Fact 4
An angle formed by two chords/two lines intersecting INSIDE a circle is equal to half the SUM of its intercepted arcs
Circle Fact 5
An angle formed by any two lines intersecting OUTSIDE of a circle is equal to half the DIFFERENCE of the intercepted arcs
Circle Fact 6
If a quadrilateral is inscribed in a circle, the opposite angles are supplementary
Circle Fact 7
A radius drawn to the point of tangency is perpendicular to the tangent
Circle Fact 8
A radius or diameter perpendicular to a chord bisects the chord and its arcs (and a radius or diameter that bisects a chord is perpendicular to that chord)
CIrcle Fact 9
Equal chords intercept equal arcs
Circle Fact 10
Parallel chords create congruent arcs
Circle Fact 11
Chords equidistant from the center of a circle are congruent
Circle Fact 12
Two tangents drawn from the same external point to a circle are congruent
Circle Fact 13
If two chords intersect in a circle, the product of their segments is equal (product of parts)
ab = cd
Circle Fact 14
If two secants are drawn from the same external point, outside x whole = outside x whole (product of outside and whole)
Circle Fact 15
If a secant and tangent are drawn from the same external point, tangent squared = outside x whole
a2 = bc
