Circle equations in the xy-plane, arc length, sector area, central angles, and completing the square to find center and radius.
50
Total questions
15
Easy
20
Medium
15
Hard
SAT circle questions split between coordinate geometry — the equation (x−h)² + (y−k)² = r², often requiring completing the square to find the center and radius — and circle measurement: arc length, sector area, and central angles as fractions of the whole.
For equations, memorize the standard form and read center and radius straight off it; when given expanded form, complete the square in x and y separately. For arcs and sectors, everything is proportional: a central angle of θ degrees captures θ/360 of the circumference and θ/360 of the area. Set up the fraction first, then multiply.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: D
Choice D is correct. The Inscribed Angle Theorem states that an inscribed angle is half the central angle that intercepts the same arc. Therefore, the inscribed angle = 80° ÷ 2 = 40°. Choice A is incorrect (this doubles the central angle instead of halving it). Choice B is incorrect (this equals the central angle, confusing central and inscribed angles). Choice C is incorrect (this divides by 4 instead of 2).
Correct answer: B
Choice B is correct. From C = 2πr, a circumference of 20π gives r = 10, so the full circle's area is π(10²) = 100π. A 72° central angle is 72/360 = 1/5 of the circle, so the sector's area is (1/5)(100π) = 20π square inches.
Choice A is incorrect. This corresponds to 1/25 of the circle rather than 1/5, as though the fraction had been squared.
Choice C is incorrect. This is the area of the whole circle, not of the 72° sector.
Choice D is incorrect. This is 4/5 of the circle — the area of the region outside the sector rather than the sector itself.
Area & Volume
Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.
Lines, Angles & Triangles
Parallel-line angle relationships, triangle angle sums, similarity and congruence, and the triangle inequality.
Right Triangles & Trigonometry
The Pythagorean theorem, special right triangles, and SOH-CAH-TOA trigonometric ratios, including the sine-cosine complement relationship.
50 Circles questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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