Circles - PSAT Math
Card 1 of 30
State the formula for the circumference of a circle with radius $r$.
State the formula for the circumference of a circle with radius $r$.
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$C=2\pi r$. Circumference equals $2\pi$ times the radius.
$C=2\pi r$. Circumference equals $2\pi$ times the radius.
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State the formula for the area of a circle with radius $r$.
State the formula for the area of a circle with radius $r$.
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$A=\pi r^2$. Area equals $\pi$ times radius squared.
$A=\pi r^2$. Area equals $\pi$ times radius squared.
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What is the relationship between diameter $d$ and radius $r$ in a circle?
What is the relationship between diameter $d$ and radius $r$ in a circle?
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$d=2r$. Diameter is twice the radius.
$d=2r$. Diameter is twice the radius.
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State the standard form of a circle with center $(h,k)$ and radius $r$.
State the standard form of a circle with center $(h,k)$ and radius $r$.
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$(x-h)^2+(y-k)^2=r^2$. Standard form shows center and radius directly.
$(x-h)^2+(y-k)^2=r^2$. Standard form shows center and radius directly.
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Identify the center and radius from $(x-3)^2+(y+4)^2=25$.
Identify the center and radius from $(x-3)^2+(y+4)^2=25$.
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Center $(3,-4)$, radius $5$. Read $(h,k)$ from $(x-h)^2+(y-k)^2$ and $r=\sqrt{25}=5$.
Center $(3,-4)$, radius $5$. Read $(h,k)$ from $(x-h)^2+(y-k)^2$ and $r=\sqrt{25}=5$.
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State the circumference of a circle with diameter $d$.
State the circumference of a circle with diameter $d$.
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$C=\pi d$. Circumference equals $\pi$ times diameter.
$C=\pi d$. Circumference equals $\pi$ times diameter.
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State the area formula for a circle with radius $r$.
State the area formula for a circle with radius $r$.
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$A=\pi r^2$. Area equals $\pi$ times radius squared.
$A=\pi r^2$. Area equals $\pi$ times radius squared.
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State the standard form equation of a circle with center $(h,k)$ and radius $r$.
State the standard form equation of a circle with center $(h,k)$ and radius $r$.
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$(x-h)^2+(y-k)^2=r^2$. Standard form shows center coordinates and radius squared.
$(x-h)^2+(y-k)^2=r^2$. Standard form shows center coordinates and radius squared.
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Find the area of a sector for $r=3$ and $\theta=120^\circ$.
Find the area of a sector for $r=3$ and $\theta=120^\circ$.
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$3\pi$. $A=\frac{120}{360}\cdot \pi(3)^2=\frac{1}{3}\cdot 9\pi=3\pi$.
$3\pi$. $A=\frac{120}{360}\cdot \pi(3)^2=\frac{1}{3}\cdot 9\pi=3\pi$.
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State the circle equation with center $(2,-1)$ and radius $4$.
State the circle equation with center $(2,-1)$ and radius $4$.
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$(x-2)^2+(y+1)^2=16$. Substitute center $(h,k)=(2,-1)$ and $r^2=16$.
$(x-2)^2+(y+1)^2=16$. Substitute center $(h,k)=(2,-1)$ and $r^2=16$.
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State the relationship between a tangent and the radius at the point of tangency.
State the relationship between a tangent and the radius at the point of tangency.
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Tangent is perpendicular to the radius. Forms a $90°$ angle at the point of tangency.
Tangent is perpendicular to the radius. Forms a $90°$ angle at the point of tangency.
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Identify the center and radius of $x^2+y^2-8x+6y=0$.
Identify the center and radius of $x^2+y^2-8x+6y=0$.
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Center $(4,-3)$, radius $5$. Complete the square: $(x-4)^2+(y+3)^2=25$.
Center $(4,-3)$, radius $5$. Complete the square: $(x-4)^2+(y+3)^2=25$.
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What is the diameter of a circle in terms of radius $r$?
What is the diameter of a circle in terms of radius $r$?
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$d=2r$. Diameter is twice the radius.
$d=2r$. Diameter is twice the radius.
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Find the measure of an inscribed angle that intercepts a $110^\circ$ arc.
Find the measure of an inscribed angle that intercepts a $110^\circ$ arc.
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$55^\circ$. Inscribed angle is half the intercepted arc: $\frac{110°}{2}=55°$.
$55^\circ$. Inscribed angle is half the intercepted arc: $\frac{110°}{2}=55°$.
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Find the distance between the centers of two circles with centers $(1,2)$ and $(4,6)$.
Find the distance between the centers of two circles with centers $(1,2)$ and $(4,6)$.
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$5$. Distance formula: $\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$.
$5$. Distance formula: $\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$.
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What is the length of a semicircle arc (not including the diameter) with radius $r$?
What is the length of a semicircle arc (not including the diameter) with radius $r$?
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$\pi r$. Half the circumference, excluding the diameter.
$\pi r$. Half the circumference, excluding the diameter.
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State the arc length formula for central angle $\theta$ (in degrees) and radius $r$.
State the arc length formula for central angle $\theta$ (in degrees) and radius $r$.
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$s=\frac{\theta}{360}\cdot 2\pi r$. Fraction of full circumference based on angle ratio.
$s=\frac{\theta}{360}\cdot 2\pi r$. Fraction of full circumference based on angle ratio.
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What is the radius of a circle in terms of diameter $d$?
What is the radius of a circle in terms of diameter $d$?
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$r=\frac{d}{2}$. Radius is half the diameter.
$r=\frac{d}{2}$. Radius is half the diameter.
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Identify the center and radius of $(x-3)^2+(y+2)^2=25$.
Identify the center and radius of $(x-3)^2+(y+2)^2=25$.
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Center $(3,-2)$, radius $5$. Read $(h,k)$ from $(x-h)^2+(y-k)^2$; $r^2=25$ so $r=5$.
Center $(3,-2)$, radius $5$. Read $(h,k)$ from $(x-h)^2+(y-k)^2$; $r^2=25$ so $r=5$.
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State the sector area formula for central angle $\theta$ (in degrees) and radius $r$.
State the sector area formula for central angle $\theta$ (in degrees) and radius $r$.
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$A=\frac{\theta}{360}\cdot \pi r^2$. Fraction of full area based on angle ratio.
$A=\frac{\theta}{360}\cdot \pi r^2$. Fraction of full area based on angle ratio.
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What is the measure of an inscribed angle that intercepts an arc of measure $m$ degrees?
What is the measure of an inscribed angle that intercepts an arc of measure $m$ degrees?
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$\frac{m}{2}$. Inscribed angle theorem: half the intercepted arc.
$\frac{m}{2}$. Inscribed angle theorem: half the intercepted arc.
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Find the center of the circle $(x+5)^2+(y-7)^2=49$.
Find the center of the circle $(x+5)^2+(y-7)^2=49$.
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$(-5,7)$. Center is $(h,k)$ where equation is $(x-h)^2+(y-k)^2$.
$(-5,7)$. Center is $(h,k)$ where equation is $(x-h)^2+(y-k)^2$.
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Find the arc length for $r=6$ and $\theta=60^\circ$.
Find the arc length for $r=6$ and $\theta=60^\circ$.
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$2\pi$. $s=\frac{60}{360}\cdot 2\pi(6)=\frac{1}{6}\cdot 12\pi=2\pi$.
$2\pi$. $s=\frac{60}{360}\cdot 2\pi(6)=\frac{1}{6}\cdot 12\pi=2\pi$.
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Find the radius of the circle $(x+5)^2+(y-7)^2=49$.
Find the radius of the circle $(x+5)^2+(y-7)^2=49$.
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$7$. $r^2=49$, so $r=\sqrt{49}=7$.
$7$. $r^2=49$, so $r=\sqrt{49}=7$.
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What is the area formula of a circle with radius $r$?
What is the area formula of a circle with radius $r$?
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$A=\pi r^2$. Area equals $\pi$ times radius squared.
$A=\pi r^2$. Area equals $\pi$ times radius squared.
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Find the area of a circle with diameter $10$.
Find the area of a circle with diameter $10$.
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$25\pi$. Use $A=\pi r^2$ with $r=5$ (half of diameter).
$25\pi$. Use $A=\pi r^2$ with $r=5$ (half of diameter).
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Find the circumference of a circle with diameter $12$.
Find the circumference of a circle with diameter $12$.
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$12\pi$. Use $C=2\pi r$ with $r=6$ (half of diameter).
$12\pi$. Use $C=2\pi r$ with $r=6$ (half of diameter).
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Find the radius if the center is $(2,3)$ and a point on the circle is $(2,11)$.
Find the radius if the center is $(2,3)$ and a point on the circle is $(2,11)$.
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$8$. Distance from $(2,3)$ to $(2,11)$ is $|11-3|=8$.
$8$. Distance from $(2,3)$ to $(2,11)$ is $|11-3|=8$.
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State the relationship between diameter $d$ and radius $r$.
State the relationship between diameter $d$ and radius $r$.
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$d=2r$. Diameter is twice the radius.
$d=2r$. Diameter is twice the radius.
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Identify the radius of the circle $(x+1)^2+(y-4)^2=49$.
Identify the radius of the circle $(x+1)^2+(y-4)^2=49$.
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$7$. Radius equals the square root of the constant term.
$7$. Radius equals the square root of the constant term.
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