Circles - SAT Math

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

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

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

Radius. Fundamental distance measurement in circles.

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

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

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

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

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

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

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

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

Circumference. Standard term for circle's perimeter.

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

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

Segment. Region between chord and its corresponding arc.

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

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

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

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

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

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

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

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

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

The diameter. Diameter passes through center, maximizing length.

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

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

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

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

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

Diameter. Standard term for longest chord through center.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circumference. Standard term for circle's perimeter.

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

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

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

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

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

The diameter. Diameter passes through center, maximizing length.

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

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

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

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

Segment. Region between chord and its corresponding arc.

Radius. Fundamental distance measurement in circles.

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

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

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

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

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

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

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

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

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

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

Diameter. Standard term for longest chord through center.

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

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

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

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

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

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

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

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

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

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

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

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

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