vocab
circumference
the perimeter of the circle
a circle has a radius of 5 inches What is its area
25 square inches
diameter
2 x Radius
what is the alternate segment theorem
that in any circle the angle between a chord and a tangent at the point of contact of the tangent is equal to the angle subtended by the chord of the alternate segement
a line segment from the center of a circle to a point on the circumference of the circle
a circle has an area of 49 square inches, what is its radius
7 feet
standard circle equation
X2+Y2=r2
what is the angle of the center theorem?
the angle formed at the center of circle by two radii is twice the measure of any inscribed angle subtended by the same arc on the circumference
Diameter
a chord passing through the center of the circle whose endpoints are on the circumference of the circle
A circle has a radius of 6 cm and a central angle of 60 degrees, what is the arc length and area of the sector
arc length: 2 cm
sector area: 6cm
π(pie)
circumference/diameter
whats the angle in a semicircle theorem?
any angle inscribed in a semicircle is always a right angle(90 degrees).
chord
a line segment whose endpoints are on the circumference of a circle
A circle has a radius of 8 inches , A tangent line is drawn from a point outside the circle. the distance from the point to the center of the circle is 17 inches. what is the the length of the tangent segment?
15 inches
area of a segment of the circle
Asector - Atriangle
whats the cyclic quadrilateral theorem?
the product of the diagonals is equals to the sum of the products of the opposite sides.
tangent line
a line that touches a single point on the circumference of a circle
Two concentric circles have a radii of 5 cm and 8 cm, what is the area of the region between the two circles?
39 cm3
area of a sector of the circle
Asector =(θ/360)(πr2)
whats the alternate segment theoreom?
the angle between a tangent and a chord at the point of tangency is equal to the angle at the alternate segment.