Unit 10 test: Circles

A circle has diameter $20$. What is its circumference? Give your answer in terms of $\pi$ (type pi).

In $\odot O$, minor arc $\overset{\frown}{AB}$ measures $142^\circ$, and $C$ is a point on the major arc. What is $m\overset{\frown}{ACB}$, in degrees?

An inscribed angle intercepts an arc of $96^\circ$. What is the measure of the angle, in degrees?

Quadrilateral $ABCD$ is inscribed in a circle, and $m\angle B = 73^\circ$. What is $m\angle D$, in degrees?

$\overline{PT}$ is tangent to $\odot O$ at $T$. The radius of the circle is $9$ and $PT = 12$. What is $OP$?

$\overline{PA}$ and $\overline{PB}$ are tangent to a circle at $A$ and $B$. If $PA = 4x - 3$ and $PB = 2x + 7$, what is $PA$?

A circle has radius $15$. How far from the center is a chord of length $24$?

Two chords intersect inside a circle. One angle they form and its vertical angle intercept arcs of $100^\circ$ and $60^\circ$. What is the measure of the angle?

Chords $\overline{AB}$ and $\overline{CD}$ intersect at $P$. If $PA = 5$, $PB = 6$ and $PC = 3$, what is $PD$?

From point $P$ outside a circle, a secant meets the circle at $A$ and $B$ with $PA = 4$ and $AB = 5$. What is the length of a tangent segment from $P$ to the circle?

Which is the equation of the circle with center $(-1, 4)$ and radius $3$?

What is the center of the circle $x^2 + y^2 - 4x + 10y + 20 = 0$? Give an ordered pair.

Find the length of a $30^\circ$ arc in a circle of radius $12$. Give your answer in terms of $\pi$.

Convert $225^\circ$ to radians. Give your answer in terms of $\pi$.

Find the area of a $45^\circ$ sector of a circle with radius $8$. Give your answer in terms of $\pi$.