Circles - ACT Math

$5$. The radius is $\sqrt{25} = 5$.

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

Center: $(3, -2)$. Center is $(h, k)$ from standard form.

Diameter = 14. Diameter is twice the radius.

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

$\theta\cdot\frac{\pi}{180}$. Multiply by $\frac{\pi}{180}$ to convert degrees.

$55^\circ$. Inscribed angle is half the intercepted arc.

Radius = 5. Radius is half the diameter.

$12\pi$. Using $A = \frac{120}{360} \pi (6)^2 = 12\pi$.

Chord Length $\approx 5$. Apply chord formula with given values.

Circumference = $\pi$ times Diameter. Circumference equals $\pi$ times diameter.

Distance = 10. Distance between parallel tangents equals diameter.

Area = $\pi r^2$. Standard formula for circular area.

Radius $\approx 5$. Using $C = 2\pi r$, solve for $r$.

Tangent: A line that touches the circle at exactly one point. Line intersecting circle at one point only.

Central angle: Angle subtended by an arc at the center. Angle formed by two radii.

Radius = 8. Use $A = \pi r^2$ and solve for $r$.

Center: $(1, -2)$, Radius: 4. Read values from standard form equation.

$(x-h)^2 + (y-k)^2 = r^2$. General equation with center $(h, k)$.

Radius = 9. Radius is square root of constant term.

Circumference = $16\pi$. Apply circumference formula with $r = 8$.

Area = $\frac{1}{2}r^2(\theta - \sin\theta)$ (in radians). Area between chord and arc.

Circumference = $2\pi r$. Circumference is proportional to radius.

Arc Length = $\theta r$ (in radians). Formula when angle is in radians.

Area = $\frac{1}{2}r^2\theta$ (in radians). Half radius squared times central angle.

Area $\approx 9\pi - 18$. Apply segment area formula.

Radius = 5. Radius is half the diameter.

Inscribed Angle = 90 degrees. Inscribed angle in semicircle is always 90°.

Chord Length $= 2r\sin(\frac{\theta}{2})$. Uses central angle and radius.