Math- Circles

Question 1

Area of a circle

Answer 1

pie x r^2

Question 2

Circumference of a circle

Answer 2

2 x pie x r

Question 3

Arc Length

Answer 3

(angle/360) x (2 x pie x r) or angle x r if the angle is in radians

Question 4

Area of a sector

Answer 4

(angle/360) x (pie x r^2) or (1/2) x r^2 x angle if the angle is in radians

Question 5

What do central angles have the same measure as?

Answer 5

Central angles have the same measure as the arcs they “carve out.” Central angles are the angle with the center of the circle.

Question 6

What is arc measure?

Answer 6

the number of degrees one turns from A to B. Or rotation along the circle from A to B. A full rotation equals 360 degrees.

Question 7

What is arc length?

Answer 7

Arc length is the actual distance you would travel along the circle from A to B.

Question 8

What are inscribed angles equal to?

Answer 8

Inscribed angles are equal to half the measure of the arcs they carve out. Inscribed angles go from one side of the circle to the other. The point isn’t on the center of the circle.

Question 9

What are angles inscribed in a semicircle always equal to?

Answer 9

They are always equal to 90 degrees. This is true because the angle inscribed in a semicircle carves out half a circle, or 180 degrees, which means the angle itself is half that, or 90 degrees.

Question 10

What is the relationship between the radius and a line tangent to the circle?

Answer 10

The line is perpendicular to the radius which means that the angle equals 90 degrees on either side of the radius.

Question 11

What is the equation of a circle in the xy plane?

Answer 11

The equation is (x - h)^2 + (y - k)^2 = r^2

where (h,k) is the center of the circle and r is the radius.