True/ False
Euclid defines a segment of a circle as the portion of a circle bounded by two radii and an arc.
False (this is actually a sector of a circle)!
The measure of the angle ___ ____ _______ is twice the measure of the angle at the circumference that stands on the same arc.
at the center
In circle ABC, diameter AB meets tangent CD at B. If m<ABC = 6x2 -12x, find x.
m<ABC = 90
6x2 - 12x = 90
6x2 - 12x - 90 = 0
6( x2 -2x -15) = 0
(x - 5)(x +3 ) = 0
x = 5 or x = -3
(Both solutions are possible, who knows exactly why ?)
Portion of a circle confined by a piece of a circle's circumference and a chord.
Segment
Ms. Lewis has a favorite color. What is it?
Purple (will give half credit for black considering it is technically a shade even though she loves it)
The angle formed by a tangent line and a diameter is a right angle.
True!
The sector of a circle is the portion of a circle bounded by __ ____ ___ __ ____.
2 radii and an arc!
In circle ABC, <ACB stands on the same arc as central <AOB. If m<AOB = 2x + 12 and m<ACB = 30 - x, find x and m<AOB.
m<AOB = 2m<ACB
2x + 12 = 2(30 - x)
2x + 12 = 60 -2x
4x = 48
x = 12
m<ADB = 2(12) + 12 = 36
The portion of a circle bounded by two radii and an arc.
Sector
Ms. Lewis has a pet turtle that has been on the board for a while. What is its' name ?
Henry
If the angle formed by 2 intersecting chords is a right angle, the point where the chords intersect is the center of the circle.
False (this could be true-- 2 perpendicular diameters that meet in the center-- or it could be false... who knows exactly how [20 bonus points]?)
A _______ ____________ is a 4-sided figure able to be inscribed in a circle.
cyclic quadrilateral
Quadrilateral ABCD is inscribed in a circle. m<A = (2/3)m<C and m<B = m<D. Find the measures of the 4 angles.
m<C = 108
m<A = 72
m <B = m<D = 90
The angle within a segment of a circle made of 2 straight lines that opens up to or "stands on" a subtending arc.
The angle IN in the segment
Cutie
All parallelograms are cyclic quadrilaterals.
False (a true parallelogram in the sense of nothing else is not, however a rectangle and a trapezia are possible)!
The _______ to a circle meets the circle at 1 point.
tangent
Tangent TG meets circle ABC at A. Chord AC is drawn. If m<CAT = (2/3) m<CAG, find the measure of minor arc AC and major arc CBA. (remember, the arc subtended arc is twice the measure of the angle at the circumference that stands on it).
Minor arc AC = 2*m<CAT = 144
Major arc CBA = 2*m<CAG = 216
The angle of the circles circumference that an angle in the segment "stands on" or opens up to.
The angle of the the segment
What is the color of the colored pencil that usually hangs on the board that is considered "true uselessness" ?
White
No cyclic quadrilaterals have diagonals that are equal to each other.
False (rectangles have diagonals that are equal to each other)!
The angle in a semicircle is ___________.
In circle ABC, AD is the diameter with center E, with the chords AB, AC, and radii BE and CE drawn. If the m<BAD = 30 and the m<DEC = 50, find m<BAC and m<BEC.
m<BAC = 55
m<BEC = 110
When a line stands on another line and creates 2 equal adjacent angles, these angles are referred to as __________.
Right
What is the expression below equal to when evaluated?
2(53 +5) -24 / 4
254