Circles Flashcards

A circle passes through points (0,0), (6,0), and (0,8). What is the radius of the circle?

Answer: 5

The hypotenuse of the right triangle formed is √(6²+8²)=10, which is the diameter, so r=5.

The equation of a circle is x² + y² − 2x + 4y − 20 = 0. What is the area of this circle?

Answer: 25π

(x−1)²+(y+2)²=20+1+4=25; r=5; area=25π.

A circle has radius r. A sector with central angle 2π/5 is cut out. What fraction of the circle's area does the sector represent?

Answer: 1/5

Fraction = θ/(2π) = (2π/5)/(2π) = 1/5.

What is the length of the longest chord of a circle with area 36π?

Answer: 12

r=6; the longest chord is the diameter = 2r = 12.

In a circle, a central angle intercepts an arc of 150°. What is the central angle in radians?

Answer: 5π/6

150° × π/180° = 150π/180 = 5π/6.

Two circles are concentric (same center). The outer circle has radius 10 and the inner circle has radius 6. What is the area of the ring (annulus) between them?

Answer: 64π

Area = π(10²) − π(6²) = 100π − 36π = 64π.

A circle has equation (x−3)²+(y+2)²=50. The point (3+t, −2) lies on the circle. What is the positive value of t?

Answer: 5√2

(3+t−3)²+(−2+2)²=50 → t²=50 → t=√50=5√2.