Drill 1 · Math · Circles, Arcs, and Angles
SAT Math: Circles, Arcs, and Angles (Drill 1) is a Math practice drill covering Circles, Arcs, and Angles. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
Circle questions on the SAT cover the standard equation of a circle, arc length, sector area, central and inscribed angles, and the relationship between a circle's radius, diameter, and circumference.
Question 1. A circle has a radius of 10 centimeters. What is the length of an arc intercepted by a central angle of 72°?
Explanation: Arc length = (θ/360)(2πr) = (72/360)(2π × 10) = (1/5)(20π) = 4π cm. The fraction 72/360 simplifies to 1/5.
Question 2. A circle has a radius of 6 inches. What is the area of a sector with a central angle of 90°?
Explanation: Sector area = (θ/360)(πr²) = (90/360)(π × 36) = (1/4)(36π) = 9π square inches. A 90° sector is one-quarter of the full circle.
Question 3. The equation x² + y² − 8x + 6y = 0 represents a circle in the xy-plane. What is the center of the circle?
Explanation: Complete the square for both x and y. Group: (x² − 8x) + (y² + 6y) = 0. Complete: (x² − 8x + 16) + (y² + 6y + 9) = 0 + 16 + 9. Simplify: (x − 4)² + (y + 3)² = 25. The center is (4, −3) and the radius is 5.
Question 4. A central angle in a circle measures 140°. What is the measure of an inscribed angle that intercepts the same arc?
Explanation: An inscribed angle is always half the central angle that intercepts the same arc. Inscribed angle = 140° ÷ 2 = 70°. This is the inscribed angle theorem.
Question 5. A circle has a circumference of 16π. What is the area of the circle?
Explanation: From the circumference: 2πr = 16π, so r = 8. Area = πr² = π(8)² = 64π.