SAT Math: Circles, Arcs, and Angles (Drill 3)

Question 1. A circle has center (3, −2) and passes through the point (7, −2). What is the equation of the circle?

• A) (x − 3)² + (y + 2)² = 4
• B) (x − 3)² + (y + 2)² = 16 ✓
• C) (x + 3)² + (y − 2)² = 16
• D) (x − 3)² + (y + 2)² = 8

Explanation: Radius = distance from (3,−2) to (7,−2) = 4. Equation: (x − 3)² + (y + 2)² = 16.

Question 2. A central angle of 150° intercepts an arc on a circle of radius 6. What is the arc length?

• A) 5π ✓
• B) 5π/2
• C) 15π
• D) π

Explanation: Arc length = (θ/360) × 2πr = (150/360) × 12π = (5/12) × 12π = 5π.

Question 3. An inscribed angle in a circle intercepts an arc of 100°. What is the measure of the inscribed angle?

• A) 100°
• B) 200°
• C) 50° ✓
• D) 25°

Explanation: An inscribed angle is half the intercepted arc: 100°/2 = 50°.

Question 4. What is the area of a sector with central angle π/3 radians and radius 9?

• A) 27π/2 ✓
• B) 3π
• C) 9π
• D) 81π/6

Explanation: Sector area = (1/2)r²θ = (1/2)(81)(π/3) = 81π/6 = 27π/2.

Question 5. A line is tangent to a circle at point P. If the radius to point P has slope 3/4, what is the slope of the tangent line?

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

Explanation: A tangent line is perpendicular to the radius at the point of tangency. The negative reciprocal of 3/4 is −4/3.