Circles Flashcards

A circle has area 25π. What is the circumference?

Answer: 10π

πr²=25π → r=5; circumference=2π(5)=10π.

Convert 210° to radians.

Answer: 7π/6

210° × (π/180°) = 210π/180 = 7π/6.

The circle x² + y² = 25 has center at the origin. Which of the following points lies inside the circle?

Answer: (3, 3)

3²+3²=18<25, so (3,3) is inside; all others satisfy x²+y² ≥ 25.

A sector has central angle 3π/2 radians and area 27π/2. What is the radius?

Answer: 3

A=½r²θ → 27π/2=½r²(3π/2)=(3πr²/4) → r²=9 → r=3.

The central angle in a circle is 5 times the inscribed angle intercepting the same arc. What is the inscribed angle?

Answer: This cannot happen; a central angle is always exactly 2× the inscribed angle

By the Inscribed Angle Theorem, the central angle is always exactly twice the inscribed angle—it can never be 5 times it.

A circle has center (−3, 2). Which equation could represent this circle?

Answer: (x + 3)² + (y − 2)² = 10

Center (−3, 2) gives (x−(−3))²+(y−2)²=r² → (x+3)²+(y−2)²=r².

The length of an arc is 8π and the radius is 16. What is the central angle in degrees?

Answer: 90°

Arc = (θ/360°)·2πr → 8π = (θ/360°)·32π → θ/360° = 1/4 → θ = 90°.