Circles — Geometry and Trigonometry

Questions in this quiz (10)

1. $$(x-3)^2+(y+1)^2=100$$In the $$xy$$-plane, the graph of the equation above is a circle. Point $$P$$ on the circle has coordinates $$(13,-1)$$. If $$PQ$$ is a diameter of the circle, what are the coordinates of $$Q$$?

   • $$(-7,-1)$$
   • $$(-7,1)$$
   • $$(3,-11)$$
   • $$(3,9)$$

2. Point $$A$$ lies on a unit circle in the $$xy$$-plane and has coordinates $$(1,0)$$. Point $$B$$ is the center of the circle and has coordinates $$(0,0)$$. Point $$C$$ also lies on the circle and has coordinates $$(t,1)$$, where $$t$$ is a constant. Which of the following could be the positive measure of angle $$ABC$$, in radians?

   • $$\frac{45\pi}{2}$$
   • $$\frac{46\pi}{2}$$
   • $$\frac{47\pi}{2}$$
   • $$\frac{48\pi}{2}$$

3. The circle shown has center $$T$$, with the length of arc $$WZY$$ equal to $$8\pi$$, and $$a=120$$. What is the length of arc $$WXY$$?

   • $$12\pi$$
   • $$24\pi$$
   • $$14\pi$$
   • $$16\pi$$

4. In the $$xy$$-plane, the graph of the equation$$(x-1)^2+(y+3)^2=36$$is a circle. The point $$(k,3)$$, where $$k$$ is a constant, lies on this circle. What is one possible value of $$k$$?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

5. An angle has a measure of $$\frac{7\pi}{18}$$ radians. What is the measure of the angle in degrees?

   • $$50^\circ$$
   • $$65^\circ$$
   • $$70^\circ$$
   • $$75^\circ$$

6. Point $$P$$ is the center of the circle above, and the measure of $$\angle PQR$$ is $$40^\circ$$. If the length of $$PS$$ is $$9$$, what is the length of arc $$\widehat{QR}$$?

   • $$2\pi$$
   • $$4\pi$$
   • $$5\pi$$
   • $$7\pi$$

7. A circle has center $$O$$, and points $$A$$ and $$B$$ lie on the circle. The central angle $$\angle AOB$$ measures $$45^\circ$$, and the circumference of the circle is $$40$$ inches. What is the length of minor arc $$AB$$?

   • $$5$$
   • $$6$$
   • $$7.5$$
   • $$10$$

8. Question

   • $$3$$
   • $$4$$
   • $$5$$
   • $$7$$

9. The circle shown has center $$C$$, circumference $$120\pi$$, and diameters $$JL$$ and $$KM$$. The length of arc $$JK$$ is three times the length of arc $$KL$$. What is the length of arc $$JM$$?

   • $$15\pi$$
   • $$30\pi$$
   • $$45\pi$$
   • $$60\pi$$

10. Circle $$P$$ is defined by the equation$$(x-5)^2+(y+1)^2=16$$Circle $$Q$$ is the result of shifting circle $$P$$ left $$7$$ units and up $$4$$ units. The radius of circle $$Q$$ is $$3$$ times the radius of circle $$P$$. Which equation defines circle $$Q$$?

    • $$(x-12)^2+(y+5)^2=48$$
    • $$(x+2)^2+(y-3)^2=48$$
    • $$(x-12)^2+(y+5)^2=144$$
    • $$(x+2)^2+(y-3)^2=144$$