SAT Math: Circles, Arcs, and Angles (Drill 2)

Question 1. Which equation represents a circle with center (−1, 5) and radius 3?

• A) (x + 1)² + (y − 5)² = 3
• B) (x − 1)² + (y + 5)² = 9
• C) (x + 1)² + (y − 5)² = 9 ✓
• D) (x − 1)² + (y − 5)² = 9

Explanation: Standard form: (x − h)² + (y − k)² = r². With center (−1, 5) and r = 3: (x + 1)² + (y − 5)² = 9. Choice A uses r instead of r².

Question 2. A circle has a radius of 12. What is the length of an arc subtended by a central angle of π/3 radians?

• A) 4π ✓
• B) 6π
• C) 12π
• D) 36π

Explanation: Arc length = rθ = 12(π/3) = 4π.

Question 3. A circle has its center at the origin. A radius drawn to the point (8, 6) has a slope of 3/4. What is the slope of the tangent line at (8, 6)?

• A) 3/4
• B) 4/3
• C) −3/4
• D) −4/3 ✓

Explanation: A tangent is perpendicular to the radius. Perpendicular slopes are negative reciprocals: −4/3.

Question 4. A sector of a circle with radius 10 has a central angle of 2π/5 radians. What is the area of the sector?

• A) 10π
• B) 20π ✓
• C) 40π
• D) 100π

Explanation: Sector area = (1/2)r²θ = (1/2)(100)(2π/5) = 100π/5 = 20π.

Question 5. The equation (x − 3)² + (y − 4)² = 25 represents a circle. Which point lies on the circle?

• A) (3, 4)
• B) (1, 1)
• C) (5, 4)
• D) (3, 9) ✓

Explanation: Test (3, 9): (3−3)² + (9−4)² = 0 + 25 = 25. ✓ (3, 4) is the center, not on the circle.