PSAT Circles Practice

The radius of a given circle is increased by 20%. What is the percent increase of the area of the circle.

• 20%

• 40%

• 44%

• 100%

• 144%

A circle is inscribed inside a square. If a point inside the square is selected at random, what is the probability that the point will also be inside the circle?

• $\frac{\pi}{4}$

• $\frac{3}{4}$

• $\frac{\pi}{6}$

• $\frac{5}{6}$

A circle has a center at (5, 5) and a radius of 2. If the format of the equation for the circle is (x + A)² + (y + B)² = C, what is C?

If the center of a circle is at (0, 4) and the diameter of the circle is 6, what is the equation of that circle?

• $x^2+\left(y-4\right)^2=36$

• $x^2+\left(y-4\right)^2=9$

• $x^2+y^2=9$

• $\left(x-4\right)^2+y^2=9$

• $\left(x-4\right)^2+y^2=36$

What is the radius of a circle with the equation
 

 $x\left(x-8\right)+y\left(y-6\right)=24?$  

• 4

• 6

• 7

• 8

• 3

A circle has its origin at (0, 0). The point (5, 7) is on the edge of the circle. What is the radius of the circle?

• $r=\sqrt{74}$

• $r=4\sqrt{21}$

• There is not enough information

• $r=6\sqrt{2}$

• $r=2\sqrt{18}$

In the figure above, a circle is centered at point C and a line is tangent to the circle at point B. What is the equation of the line?

• $5x-2y=41$

• $2x+5y=-1$

• $5x+2y=29$
  

• $x+y=4$
  

• $2x-5y=29$

If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?

The perimeter of a circle is 36 π. What is the diameter of the circle?

A circle with an area of 13π in² is centered at point C. What is the circumference of this circle?

• $\pi\sqrt{13}$

• $26\pi$

• $2\pi\sqrt{13}$

• $13\pi$

• $\pi\sqrt{26}$