CIRCUMFERENCE & AREA
A circle has radius 9. Find the circumference.
18π
Find the arc length of a 60∘ arc in a circle with radius 6.
2π or 6.28
An inscribed angle intercepts an arc of 80∘. Find the angle measure.
40 degrees
A tangent from a point outside the circle has length 12. Find the length of the other tangent from the same point.
12
Write the center and radius of: (x−3)2+(y+2)2=25
A: Center (3,−2), radius 5
A circle has diameter 12. Find the area.
36π
Find the area of a 90∘ sector in a circle with radius 10.
25π or 78.54
A central angle is 100∘. Find the measure of the inscribed angle intercepting the same arc.
50 degrees
Two chords intersect inside a circle. Segments: 4 and 6 on one chord, 3 and x on the other. Solve for x.
8
Write the equation of a circle with center (2,−1) and radius 7.
(x−2)2+(y+1)2=49
A circle has circumference 32π. Find the radius.
r=16
A circle has radius 15. An arc length is 6π. Find the central angle.
72 degrees
Two inscribed angles intercept the same arc. One is 35∘. Find the other.
35 degrees
A secant has outside segment 5 and whole secant 20. A tangent from the same point has length x. Find x. Use: t2=(outside)(whole)
10
Expand: (x+4)2+(y−3)2=36
x2+8x+16+y2−6y+9=36
A circle’s area is 49π. Find the diameter.
d=14
A sector has area 12π in a circle with radius 6. Find the central angle.
120 degrees
An angle formed by a tangent and a chord is 45∘. Find the measure of the intercepted arc.
θ=90∘
Two secants:
Outside 4, whole 12
Outside 6, whole x Find x.
8
A perpendicular bisector of a chord passes through the center. A chord is 16 units long and 6 units from the center. Find the radius. Use right triangle: half-chord = 8
r=10
A circle’s circumference is equal to its area. Find the radius. Solve: 2πr=πr2
r=2
A circle has circumference 48π. A central angle intercepts an arc of length 4π. Find the angle measure.
30 degrees
An angle formed outside the circle by two secants is 25∘. The far arc is 150∘. Find the near arc. Use: outside angle = ½(far − near)
100 degrees
Two chords intersect. Segments: x and x+3 on one chord, 5 and 7 on the other. Solve for x.
5
A triangle is inscribed in a circle. The diameter is 20. One angle of the triangle is 90∘. Find the hypotenuse.
20 Thales’ Theorem