Equation of a Circle
Arcs and Sectors
Tangent Lines
Inscribed Angles
100
Which formula is the equation of a circle derived from?
(x-h)^2+(y-k)^2=r^2
Pythagorean Theorem!
a^2+b^2=c^2
(x-h)^2+(y-k)^2=r^2
100
Which TWO formulas determine the Arc Length of a circle and Area of a Sector circle?
(in other words)
an Arc Length is PART OF the __________
Area of a Sector is PART OF the __________
CIRCUMFERENCE & AREA
100
When a line is tangent to a circle, what angle is created?
Tangent Lines are perpendicular to the radius. They create 90o angles
100
How is the inscribed angle related to the intercepted arc?
1) The inscribed angle is 1/2 the intercepted arc
OR
2) The intercepted arc is double the inscribed angle measure
200
Write the standard equation of a circle given...
Center (4,3) Radius: r = 8
(x-4)^2+(y-3)^2=64
200
What is the measure of arc FCD
Arc FCD = 236o
200
Determine the missing angle measure given. All lines that appear tangent are tangent!
140o
200
Determine the measure of the arc DGF
Arc DGF = 226o
200
Write the standard equation of a circle given...
Center (-5,0) Radius: r = 4
(x+5)^2+y^2=16
200
What is the measure of arc PSQ?
Arc PSQ = 289o
200
Directions: The quadrilaterals circumscribes a circle. What is the perimeter of the quadrilateral?
70mm
200
Determine the missing angle measure given the inscribed angles
x = 31o
300
Find the center and radius of each circle
(x-4)^2+(y+9)^2=36
Center: (4,-9) Radius: r = 6
300
Determine the Arc Length of Arc QP given the central angle of 109o and the radius equals 14.
(round your answer to the nearest tenth)
Arc Length = 26.6 units
300
Determine whether a tangent line is shown in the diagram
No. A tangent line is not shown.
Proven by the Converse of the Pythagorean Theorem
4.5^2+10^2=12^2
120.25!=144
300
Determine the measure of arc BC
Arc BC = 86o
400
Write the standard equation of a circle given the center and passes through the given point
Center (5,9); Point (2,9)
(x-5)^2+(y-9)^2=9
400
What is the Area of the Shaded Region (Area of the Sector
Area of the Sector = 2563 units2
(100 points) Area of the non-shaded region = 652 units2
400
Lines that appear tangent ARE tangent to the circle.
Determine the radius of the circle.
x = 9
400
Determine all the missing inscribed angles given the quadrilateral in the circle
mangleP = 72^o
mangleR = 108^o
mangleS = 87^o