SAT Math Flashcards: Circles

What this deck covers

This deck focuses on Circles, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify the longest chord in a circle.

Answer: The diameter. Diameter passes through center, maximizing length.

Flashcard 2: Identify the circumference of a circle with radius 12.

Answer: $C = 24\pi$. Apply $C = 2\pi r$ with $r = 12$.

Flashcard 3: What is the term for the distance from the center to any point on the circle?

Answer: Radius. Fundamental distance measurement in circles.

Flashcard 4: Calculate the area when the radius is 4.

Answer: $A = 16\pi$. Apply $A = \pi r^2$ with $r = 4$.

Flashcard 5: Identify the radius if the diameter of a circle is 10.

Answer: $r = 5$. Radius equals half the diameter.

Flashcard 6: Determine the length of an arc with radius 4 and angle 90°.

Answer: $\text{Arc Length} = 2\pi$. Use $s = r\theta$ with $\theta = \frac{\pi}{2}$.

Flashcard 7: Identify the center and radius of $x^2 + y^2 = 49$.

Answer: Center is $(0, 0)$, $r = 7$. Origin center with $r = \sqrt{49} = 7$.

Flashcard 8: What is the formula for the angle of an inscribed angle?

Answer: Half the measure of the intercepted arc. Inscribed angle theorem relates to intercepted arc.

Flashcard 9: Find the circumference if the radius of a circle is 7.

Answer: $C = 14\pi$. Apply $C = 2\pi r$ with $r = 7$.

Flashcard 10: State the formula for the length of an arc.

Answer: $\text{Arc Length} = r\theta$. Formula with angle $\theta$ in radians.

Flashcard 11: Find the center of the circle: $(x-5)^2 + (y+3)^2 = 25$.

Answer: Center = $(5, -3)$. The center coordinates are $(h,k)$ from $(x-h)^2 + (y-k)^2 = r^2$.

Flashcard 12: What is the formula for the equation of a circle in standard form?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Standard form with center $(h,k)$ and radius $r$.

Flashcard 13: State the definition of a secant line in a circle.

Answer: A line that intersects a circle at two points. Distinguishes secant from tangent lines.

Flashcard 14: What is the formula for the equation of a circle in general form?

Answer: $Ax^2 + Ay^2 + Dx + Ey + F = 0$. The expanded form where $A$, $D$, $E$, and $F$ are constants.

Flashcard 15: What is the formula for the angle of an inscribed angle?

Answer: Half the measure of the intercepted arc. Inscribed angle theorem relates to intercepted arc.

Flashcard 16: What is the formula for the area of a circle?

Answer: $A = \pi r^2$. Standard formula for area using radius squared.

Flashcard 17: Determine the radius of the circle $(x - 5)^2 + (y + 6)^2 = 64$.

Answer: $r = 8$. Radius equals $\sqrt{64} = 8$.

Flashcard 18: Calculate the area of a sector with radius 3 and angle 30°.

Answer: $A = \frac{3\pi}{2}$. Use $A = \frac{1}{2}r^2\theta$ with $\theta = \frac{\pi}{6}$.

Flashcard 19: Find the radius if the circumference is $20\pi$.

Answer: $r = 10$. Solve $20\pi = 2\pi r$ to get $r = 10$.

Flashcard 20: What is the formula for the equation of a circle in standard form?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Standard form with center $(h,k)$ and radius $r$.

Flashcard 21: What is the length of an arc with radius 5 and angle 60°?

Answer: $\text{Arc Length} = \frac{5\pi}{3}$. Use $s = r\theta$ where $\theta = \frac{\pi}{3}$ radians.

Flashcard 22: What defines a concentric circle?

Answer: Circles with the same center but different radii. Circles sharing center point with different sizes.

Flashcard 23: Identify the area of a circle with diameter 8.

Answer: $A = 16\pi$. Use $A = \pi r^2$ with $r = 4$.

Flashcard 24: What is the radius of the circle $(x + 1)^2 + (y - 4)^2 = 25$?

Answer: $r = 5$. Radius equals $\sqrt{25} = 5$.

Flashcard 25: Identify the center and radius of $x^2 + y^2 = 49$.

Answer: Center is $(0, 0)$, $r = 7$. Origin center with $r = \sqrt{49} = 7$.

Flashcard 26: Determine the diameter given the circle's circumference is $31.4$ cm.

Answer: Diameter = $10$ cm. Using $C = 2\pi r$: $31.4 = 2\pi r$, so $r = 5$, diameter = $10$.

Flashcard 27: Calculate the area when the radius is 4.

Answer: $A = 16\pi$. Apply $A = \pi r^2$ with $r = 4$.

Flashcard 28: Identify the center of the circle $(x - 3)^2 + (y + 2)^2 = 16$.

Answer: Center is $(3, -2)$. Center coordinates are $(h,k) = (3,-2)$.

Flashcard 29: Identify the circumference of a circle with radius 12.

Answer: $C = 24\pi$. Apply $C = 2\pi r$ with $r = 12$.

Flashcard 30: What is the term for a circle's distance across through the center?

Answer: Diameter. Standard term for longest chord through center.

Flashcard 31: What is the term for the distance from the center to any point on the circle?

Answer: Radius. Fundamental distance measurement in circles.

Flashcard 32: What is the term for a circle's boundary?

Answer: Circumference. Standard term for circle's perimeter.

Flashcard 33: What is the formula for the area of a circle?

Answer: $A = \pi r^2$. Standard formula for area using radius squared.

Flashcard 34: What defines a concentric circle?

Answer: Circles with the same center but different radii. Circles sharing center point with different sizes.

Flashcard 35: Find the circumference if the radius of a circle is 7.

Answer: $C = 14\pi$. Apply $C = 2\pi r$ with $r = 7$.

Flashcard 36: Find the diameter if the circumference is $18\pi$.

Answer: $d = 18$. Solve $18\pi = 2\pi r$ to get $r = 9$, so $d = 18$.

Flashcard 37: State the definition of a tangent line to a circle.

Answer: A line that touches a circle at exactly one point. Key property distinguishing tangent from secant lines.

Flashcard 38: Calculate the area of a sector with radius 3 and angle 30°.

Answer: $A = \frac{3\pi}{2}$. Use $A = \frac{1}{2}r^2\theta$ with $\theta = \frac{\pi}{6}$.

Flashcard 39: What is the relationship between a radius and a tangent?

Answer: They are perpendicular at the point of tangency. Radius and tangent form $90°$ angle at contact point.

Flashcard 40: Identify the radius if the diameter of a circle is 10.

Answer: $r = 5$. Radius equals half the diameter.

Flashcard 41: What is the formula for the circumference of a circle?

Answer: $C = 2\pi r$. The distance around a circle equals $2$ times $\pi$ times the radius.

Flashcard 42: Identify the equation of a circle with center $(0, 0)$ and radius 9.

Answer: $x^2 + y^2 = 81$. Standard form equation with $r^2 = 81$.

Flashcard 43: What defines a chord in a circle?

Answer: A line segment with both endpoints on the circle. Distinguishes chord from other circle segments.

Flashcard 44: Identify the longest chord in a circle.

Answer: The diameter. Diameter passes through center, maximizing length.

Flashcard 45: What is the formula for the circumference of a circle?

Answer: $C = 2\pi r$. Standard formula relating circumference to radius.

Flashcard 46: Find the diameter if the circumference is $18\pi$.

Answer: $d = 18$. Solve $18\pi = 2\pi r$ to get $r = 9$, so $d = 18$.

Flashcard 47: State the definition of a tangent line to a circle.

Answer: A line that touches a circle at exactly one point. Key property distinguishing tangent from secant lines.

Flashcard 48: Determine the radius if the diameter is 20.

Answer: $r = 10$. Radius equals half the diameter.

Flashcard 49: State the formula to find the arc length of a circle.

Answer: $L = \frac{\theta}{360} \times 2\pi r$. Arc length equals the fraction of the circle times the circumference.

Flashcard 50: What distinguishes a minor arc from a major arc?

Answer: A minor arc is less than 180°; a major arc is more. Classification based on arc's angular measure.

Flashcard 51: What is the length of an arc with radius 5 and angle 60°?

Answer: $\text{Arc Length} = \frac{5\pi}{3}$. Use $s = r\theta$ where $\theta = \frac{\pi}{3}$ radians.

Flashcard 52: State the formula for the length of an arc.

Answer: $\text{Arc Length} = r\theta$. Formula with angle $\theta$ in radians.

Flashcard 53: State the definition of a secant line in a circle.

Answer: A line that intersects a circle at two points. Distinguishes secant from tangent lines.

Flashcard 54: What is the radius of the circle $(x + 1)^2 + (y - 4)^2 = 25$?

Answer: $r = 5$. Radius equals $\sqrt{25} = 5$.

Flashcard 55: Calculate the radius if the area is $36\pi$.

Answer: $r = 6$. Solve $36\pi = \pi r^2$ to get $r = 6$.

Flashcard 56: What is the term for the line that divides a chord into two equal parts?

Answer: Perpendicular bisector. Property of line from center to chord midpoint.

Flashcard 57: What is the name for the part of a circle bounded by a chord and the arc?

Answer: Segment. Region between chord and its corresponding arc.

Flashcard 58: Identify the area of a circle with diameter 8.

Answer: $A = 16\pi$. Use $A = \pi r^2$ with $r = 4$.

Flashcard 59: What is the formula for the equation of a circle centered at the origin?

Answer: $x^2 + y^2 = r^2$. Special case of standard form with center at origin.

Flashcard 60: What defines a chord in a circle?

Answer: A line segment with both endpoints on the circle. Distinguishes chord from other circle segments.

Flashcard 61: What is the term for a circle's boundary?

Answer: Circumference. Standard term for circle's perimeter.

Flashcard 62: What distinguishes a minor arc from a major arc?

Answer: A minor arc is less than 180°; a major arc is more. Classification based on arc's angular measure.

Flashcard 63: Identify the radius given the circle's equation: $(x-3)^2 + (y+2)^2 = 16$.

Answer: Radius = $4$. In standard form $(x-h)^2 + (y-k)^2 = r^2$, the radius is $\sqrt{16} = 4$.

Flashcard 64: Find the circumference of a circle with diameter 14.

Answer: $C = 14\pi$. Apply $C = \pi d$ with $d = 14$.

Flashcard 65: What is the term for a circle's distance across through the center?

Answer: Diameter. Standard term for longest chord through center.

Flashcard 66: Identify the center of the circle $(x - 3)^2 + (y + 2)^2 = 16$.

Answer: Center is $(3, -2)$. Center coordinates are $(h,k) = (3,-2)$.

Flashcard 67: What is the formula for the area of a sector with radius $r$ and angle $\theta$?

Answer: $A = \frac{1}{2}r^2\theta$. Formula for sector area with angle in radians.

Flashcard 68: Determine the radius of the circle $(x - 5)^2 + (y + 6)^2 = 64$.

Answer: $r = 8$. Radius equals $\sqrt{64} = 8$.

Flashcard 69: What is the relationship between a radius and a tangent?

Answer: They are perpendicular at the point of tangency. Radius and tangent form $90°$ angle at contact point.

Flashcard 70: What is the term for the line that divides a chord into two equal parts?

Answer: Perpendicular bisector. Property of line from center to chord midpoint.

Flashcard 71: What is the formula for the area of a circle?

Answer: $A = \pi r^2$. Area equals $\pi$ times the radius squared.

Flashcard 72: Find the circumference of a circle with diameter 14.

Answer: $C = 14\pi$. Apply $C = \pi d$ with $d = 14$.

Flashcard 73: Determine the length of an arc with radius 4 and angle 90°.

Answer: $\text{Arc Length} = 2\pi$. Use $s = r\theta$ with $\theta = \frac{\pi}{2}$.

Flashcard 74: Determine the radius if the diameter is 20.

Answer: $r = 10$. Radius equals half the diameter.

Flashcard 75: Calculate the diameter if the radius is $7$ cm.

Answer: Diameter = $14$ cm. Diameter equals twice the radius: $2 \times 7 = 14$ cm.

Flashcard 76: State the formula for the sector area of a circle.

Answer: $A = \frac{\theta}{360} \times \pi r^2$. Sector area equals the fraction of the circle times the total area.

Flashcard 77: What is the standard form equation of a circle?

Answer: $(x-h)^2 + (y-k)^2 = r^2$. Where $(h,k)$ is the center and $r$ is the radius.

Flashcard 78: Identify the equation of a circle with center $(0, 0)$ and radius 9.

Answer: $x^2 + y^2 = 81$. Standard form equation with $r^2 = 81$.

Flashcard 79: What is the name for the part of a circle bounded by a chord and the arc?

Answer: Segment. Region between chord and its corresponding arc.

Flashcard 80: What is the formula to find the diameter of a circle given the radius?

Answer: $d = 2r$. Diameter is twice the radius.

Flashcard 81: What is the formula for the circumference of a circle?

Answer: $C = 2\pi r$. Standard formula relating circumference to radius.

Flashcard 82: What is the formula to find the diameter of a circle given the radius?

Answer: $d = 2r$. Diameter is twice the radius.

Flashcard 83: What is the formula for the area of a sector with radius $r$ and angle $\theta$?

Answer: $A = \frac{1}{2}r^2\theta$. Formula for sector area with angle in radians.

Flashcard 84: Calculate the radius if the area is $36\pi$.

Answer: $r = 6$. Solve $36\pi = \pi r^2$ to get $r = 6$.

Flashcard 85: Find the radius if the circumference is $20\pi$.

Answer: $r = 10$. Solve $20\pi = 2\pi r$ to get $r = 10$.