Geometry Unit 5: Circles

Arc length, sector area, radians, inscribed angles, chords and tangents, and the equation of a circle. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Arc lengthNo calculator

A circle has radius 9. What is the length of an arc with central angle $80^\circ$?

1. $18\pi$
2. $2\pi$
3. $8\pi$
4. $4\pi$

Question 2

Sector areaNo calculator

What is the area of a sector of a circle with radius 6 and central angle $150^\circ$?

1. $\frac{15\pi}{2}$
2. $5\pi$
3. $30\pi$
4. $15\pi$

Question 3

Inscribed anglesNo calculator

An inscribed angle intercepts an arc of $110^\circ$. What is the measure of the inscribed angle?

1. $55$
2. $110$
3. $70$
4. $220$

Question 4

Equations of circlesNo calculator

Which is the equation of the circle with center $(-3,4)$ and radius 5?

1. $(x+3)^{2}+(y-4)^{2}=25$
2. $(x+3)^{2}+(y-4)^{2}=5$
3. $(x-3)^{2}+(y+4)^{2}=25$
4. $(x-3)^{2}+(y-4)^{2}=25$

Question 5

Equations of circlesNo calculator

What are the center and radius of the circle $x^2+y^2-6x+10y+18=0$?

1. Center $(-3,5)$, radius $4$
2. Center $(3,-5)$, radius $16$
3. Center $(3,-5)$, radius $\sqrt{18}$
4. Center $(3,-5)$, radius $4$

Question 6

Tangent linesNo calculator

A line through $P$ is tangent to a circle at $T$. The radius is 8 and $PT=15$. How far is $P$ from the center?

1. $\sqrt{161}$
2. $7$
3. $17$
4. $23$

Question 7

ChordsNo calculator

Two chords of a circle intersect. One is cut into pieces of 4 and 9. The other is cut into pieces of 6 and $x$. What is $x$?

1. $11$
2. $13.5$
3. $6$
4. $3$

Question 8

Radian measureNo calculator

What is $225^\circ$ in radians?

1. $\frac{5\pi}{2}$
2. $\frac{4\pi}{5}$
3. $\frac{3\pi}{4}$
4. $\frac{5\pi}{4}$

Question 9

Inscribed quadrilateralsNo calculator

A quadrilateral is inscribed in a circle. One of its angles measures $72^\circ$. What does the opposite angle measure?

1. $72$
2. $108$
3. $144$
4. $36$

Question 10

Equations of circlesNo calculator

Where is the point $(5,-2)$ compared with the circle $(x-1)^2+(y+1)^2=17$?

1. On the circle
2. At the center
3. Outside the circle
4. Inside the circle

Question 11

Circumference and areaNo calculator

A circle has area $49\pi$. What is its circumference?

1. $49\pi$
2. $14\pi$
3. $98\pi$
4. $7\pi$

Question 12

Radian measureNo calculator

A central angle of a circle with radius 10 cm cuts off an arc 12 cm long. What is the angle in radians?

1. $\frac{5}{6}$
2. $12$
3. $0.6$
4. $1.2$