SAT Math: Circles 02

Which of the following is an equation of a circle in the xy-plane with center $(-3,-3)$ , and a radius of $\sqrt{170}$ ?

$(x+3)^2 + (y+3)^2 = \sqrt{170}$

$(x-3)^2 + (y-3)^2 = 170$

$(x+3)^2 + (y+3)^2 = 170$

$(x+3)^2 + (y-3)^2 = \sqrt{170}$

$\overline{AC}$ is a diameter. If $\widehat{BC}$ is $60 \textdegree$ , what is the measure of $\angle ADB$ ?

$60 \textdegree$

$180 \textdegree$

$120 \textdegree$

$40 \textdegree$

The two semicircles in the figure have centers $U$ and $V$ . If $UV=15$ , what is the total length of the darkened curve?

$7.5 \pi$

$15 \pi$

$12 \pi$

$3 \pi$

Triangle $ABC$ is inscribed in the circle with center $D$ , and diameter $\overline{AB}$ . If $\overline{BC} = \overline{DB}$ , what is the measure of $\angle DCB$ ?

$30 \textdegree$

$45 \textdegree$

$60 \textdegree$

$90 \textdegree$

$\overline{AD} = 5$ . The diameter of circle $B$ is $26$ . What is the length of $\overline{BC}$ ?

$5$

$12$

$13$

$24$

In the figure above, point $M$ is the center of the circle. Line segments $JL$ and $KL$ are tangent to the circle at points $J$ and $K$ , respectively, and intersect at point $L$ , as shown. If the circumference of the circle is $110$ , what is the length of minor arc $\widehat{JK}$ ?