circle facts pt.1
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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