Circles

Question 1

Area of a circle

Answer 1

πr²

Question 2

Circumference of a circle

Answer 2

2πr

Question 3

Arc length in degrees given the arc measure and radius

Answer 3

(Θ/360)*2πr since Θ/360 determines how much of the total circle the arc is and 2πr is the circumference

Question 4

Arc length in radians given the arc measure and radius

Answer 4

Θr * in (Θ/2π)2πr the 2π cuts off (remember 360=2π)

Question 5

Area of a sector in degrees given its arc measure and radius

Answer 5

(Θ/360)*πr²

Question 6

Area of a sector in radians given its arc measure and radius

Answer 6

Θr²/2 since in (Θ/2π)πr², the π’s cut off*

Question 7

Relation between a central angle and the arc measure they carve out

Answer 7

They are =

Question 8

Difference between arc length and arc measure

Answer 8

Arc length is the distance (circumference) between two points in a circle while arc measure is the degrees if two points in a circle was the end points of a central angle

Question 9

Difference between inscribed angle and arc measure they carve out

Answer 9

Inscribed angle= 0.5 arc measure

Question 10

The relation between the radius and the circle’s tangent it touches

Answer 10

They are perpendicular

Question 11

General equation of a circle

Answer 11

(x-h)²+(y-k)²=r² similar to the distance formula √((x2-x1)^2+(y2-y1)^2) since they are both derived from the Pythagorean theorem

Question 12

Arc measure of an angle inscribed in a semi-circle

Answer 12

90 degrees