Khan Academy Geometry

162°

A circle has a circumference of 10. It has an arc of length 9/2. What is the central angle of the arc, in degrees?

60° --------------- 1. θ/360 = s/c 2. θ/360 = 1/6

A circle has a circumference of 6. It has an arc of length 1. What is the central angle of the arc, in degrees?

4π ------------------- 1. c = 2πr = 2π(10) = 20π 2. θ/360 = s/c 3. 72/360 = s/20π 4. 1/5 = s/20π 5. 1/5 x 20π = s 6. 4π = s

A circle has a radius of 10. An arc in this circle has a central angle of 72°. What is the length of the arc?

1.05

A circle has a radius of 3. An arc in this circle has a central angle of 20°. What is the length of the arc?

9π/2 -------------- https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-arc-length-deg/e/circles_and_arcs?modal=1

A circle has a radius of 5. An arc in this circle has a central angle of 162°. What is the length of the arc?

81π ------------------------ 1. θ/2π = As/Ac (2π bc 2π or 360° in a circle) 2. 120/360 = 27π/x

A circle has a sector with area 27π and a central angle of 120°. What is the area of the circle?

c

A circle is centered at M (0, 0). The point B (-4, √5) is on the circle. Where does the point A (5, -1) lie? a) inside the circle b) on the circle c) outside the circle

b

A circle is centered at O (0, 0) and has a radius of √29. Where does the point T (5, -2) lie? a) inside the circle b) on the circle c) outside the circle

(45/4)π ------------------- 1. θ/2π = As/Ac (2π bc 2π or 360° in a circle) 2. (9/10)π / 2π = As/25π 3. 9/20 = As/25π 4. 9/20 x 25π = As 5. (45/4)π = As

A circle with area 25π has a sector with a central angle of 9/10π radians. What is the area of the sector?

(3/2)π = As --------------------------- 1.θ/360 = As/Ac (As = area of sector; Ac = area of entire circle) 2. 60/360 = As/9π 3. 1/6 x 9π = As 4. (3/2)π = As

A circle with area 9π has a sector with a central angle of 60°. What is the area of the sector?

11

A circle with circumference 12 has an arc with a 330° central angle. What is the length of the arc?

1 ----------------- 1. The ratio between the arc's central angle θ and 360° is equal to the ratio between the arc length 's' and the circle's circumference 'c' 2. θ/360 = s/c 3. 60°/360° = s/6 4. 1/6 = s/6 5. 1/6 x 6 = s 6. 1 = s

A circle with circumference 6 has an arc with a 60° central angle. What is the length of the arc?

20π ------------------------ 1. Ac = πr^2-> Ac = 100π 2. θ/2π = As/Ac (2π bc 2π or 360° in a circle) 3. (2/5π)/(2π) = As/100π 4. 1/5 = As/100π 5. 1/5 x 100π = As 6. 20π = As

A circle with radius 10 has a sector with a central angle of 2/5π radians. What is the area of the sector?

C =(-14, 3) --------------------- 1. -6 - -2= -4 2. -4 = 1/3 x h-> h = -12 (horizontal displacement) 3. -1 - -3 = 2 4. 2 = 1/3 x v -> v = 6 (vertical displacement) 5. x coordinate: -2 + (-12) = -14 y coordinate: -3 + 6 = 3 C = (-14, 3)

A, B, and C are collinear, and B is between A and C. The ratio of AB to AC is 1 : 3. If A is at (-2, -3) and B is at (-6, -1), what are the coordinates of point C?

C = (3, 9)

A, B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1. If A is at (1, -9) and B is at (2, 0), what are the coordiantes of point C?

C = (-2, -8) ----------------------- 1. 1 -7 = *-*6 (horizontal distance; remember to pay attention to negatives) 2. -6 x 1/2 = -3 3. -6 - (-2) = *-*4 (vertical distance) 4. -4 x 1/2 = -2 5. x coordinate: 1 + (-3) = -2 y coordinate: -6 + (-2) = -8 C = (-2, -8)

A. B, and C are collinear, and B is between A and C. The ratio of AB to BC is 2: 1. If A is at (7, -2) and B is at (1, -6), what are the coordinates of point C?

3/10 ---------------- 1. central angle θ/circumference 2. (3π/5)/2π 3. fraction = 3/10

An arc subtends a central angle measuring 3π/5 radians. What fraction of the circumference is this arc?

7/8 ------------------- 1. central angle θ/circumference 2. (7π/4)/2π 3. fraction = 7/8

An arc subtends a central angle measuring 7π/4 radians. What fraction of the circumference is this arc?

23π/18

Convert the angle θ = 230° to radians. θ = _____ radians

207° --------------- 1. Angle in Degrees = 180°/π x Angle in Radians 2. Angle in Degrees = 180°/π x 23π/20 3. θ = 207°

Convert the angle θ = 23π/20 radians to degrees. θ = _____

23π/12 ------------------- Angle x π/180

Convert the angle θ = 345° to radians. θ = ____ radians

160°

Convert the angle θ = 8π/9 radians to degrees θ = ____

(3, 11/2) --------------------- Midpoint formula: (X1 + X2/(2)), (Y1 + Y2/(2))

Point A is at (-1, 8) and point B is at (7, 3). What is the midpoint of line segment AB?

√8 --------------------- d = √(x1 - x2)^2 + (y1 - y2)^2

What is the distance between (-6, 4) and (-8, 6)?

r = 4/θ ---------------------- s = rθ

With an arc length of 4, write a formula for 'r' in terms of 'θ' https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-arc-length-rad/e/cc-radians-and-arc-length?modal=1