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Circle Tangents - Printable Mathematics Worksheets - Wayground

Circle Tangents

16 questions

10th - 10th Grade

Mathematics

Circle Tangents is a free printable Grade 10 mathematics worksheet that develops core circle-geometry skills through 16 items. Students identify radius, diameter, chord, tangent, secant, arcs, and points of tangency; calculate circle area, circumference, arc measures, and shaded-sector area; and use tangent relationships and right-triangle reasoning to find unknown lengths and determine whether a segment is tangent. The worksheet combines 13 multiple-choice questions with one fill-in-the-blank item and two matching activities. Students apply formulas, interpret circle diagrams, preserve answers in terms of pi when requested, round sector-area results appropriately, and connect vocabulary terms to labeled parts of a circle. It is designed for Grade 10 math instruction, independent practice, review, or formative assessment, and includes a complete answer key for efficient checking.

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Circle Tangents

Total questions: 16

Name
Class
Date
1.

What is the radius of the circle?

a)

18

b)

10

c)

9

d)

8

2.

Calculate the Area of the circle.


A =  π\pi   r2r^2  

a)

20πcm220\pi cm^2

b)

40πcm240\pi cm^2

c)

100πcm2100\pi cm^2

d)

400πcm2400\pi cm^2

3.

Find the area of this circle. Leave your answers in terms of pi. 

a)

25π25\pi


b)

5π5\pi

c)

10π10\pi

d)

100π100\pi

4.

Find the circumference. Leave your answer in terms of pi. 

 

a)

8 π\pi  

b)

4

c)

2 π\pi  

d)

4 π\pi  

5.

The radius of a circle is 4. What is the diameter?

(a)  

6.

Find the measure of the given arc.

a)


132o132^o

b)

53o53^o

c)

79o79^o

d)

200o200^o

7.

Find the measure of the given arc.

a)

147o147^o

b)

200o200^o

c)

228o228^o

d)

160o160^o

8.

Find the measure of the given arc.

a)

84o84^o

b)

42o42^o

c)

318o318^o

d)


138o138^o

9.

What is the area of the shaded SECTOR? Round to the nearest hundredth.

a)

9.42 u2

b)

113.10 u2

c)

284.3 u2

d)

452.39 u2

10.

What is the value of x if both segments are tangent to the circle?

a)

A

b)

B

c)

C

d)

D

11.

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

a)

15

b)

6

c)

-24

d)

14

12.

Determine whether segment MP is tangent to the circle.

a)

YES

b)

NO

13.
Find the length of BC.
a)
2
b)
3
c)
9
d)
14
14.
Question Image

Match the following part of the circle with its correct label.

Center

Point S

Chord

Segment XW XW‾\overline{XW}

Radius

ST‾\overline{ST}

Segment ST

Diameter

QV‾\overline{QV}

Segment QV

Tangent Line

VU‾\overline{VU}

Line VU

15.
Question Image

Match the following vocabulary term with its appropriate part of the circle.

Secant Line

Line PR

Point of Tangency

Point V

Minor Arc

∩QP\cap QP

Arc QP

Major Arc

∩RVT\cap RVT

Arc RVT

Semi-Circle

∩QXV\cap QXV

Arc QXV

16.
QS is a tangent to circle P.  Find QS.
a)
144
b)
14
c)
12
d)
13
Answer Key

Circle Tangents

Total questions: 16

1.
c)

9

2.
c)

100πcm2100\pi cm^2

3.
a)

25π25\pi


4.
d)

4 π\pi  

5.
8
6.
a)


132o132^o

7.
b)

200o200^o

8.
d)


138o138^o

9.
b)

113.10 u2

10.
b)

B

11.
a)

15

12.
b)

NO

13.
d) 14
14.

Center

 - 

Point S

, 

Chord

 - 

Segment XW XW‾\overline{XW}

, 

Radius

 - 

ST‾\overline{ST}

Segment ST

, 

Diameter

 - 

QV‾\overline{QV}

Segment QV

, 

Tangent Line

 - 

VU‾\overline{VU}

Line VU

15.

Secant Line

 - 

Line PR

, 

Point of Tangency

 - 

Point V

, 

Minor Arc

 - 

∩QP\cap QP

Arc QP

, 

Major Arc

 - 

∩RVT\cap RVT

Arc RVT

, 

Semi-Circle

 - 

∩QXV\cap QXV

Arc QXV

16.
c) 12

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FAQs

What does the Circle Tangents worksheet cover?

This Grade 10 worksheet practices identifying circle parts and calculating radius, diameter, area, circumference, arc measures, and shaded-sector area. Its 13 multiple-choice questions, fill-in-the-blank diameter item, and two matching activities also require students to apply tangent relationships, solve lengths using right-triangle reasoning, and distinguish terms such as chord, secant, minor arc, major arc, and semicircle.

How can I use this worksheet to teach circle tangents and related circle measures?

Introduce the worksheet by reviewing radius, diameter, circumference, area, arcs, and sectors with a labeled circle diagram, then model how a radius relates to a tangent at the point of tangency. Have students explain why a segment is or is not tangent before solving the unknown-length and right-triangle items. Use the matching sections afterward to reinforce the vocabulary represented in the diagrams.

What mistakes should I watch for when students complete this circle-geometry worksheet?

Watch for students confusing radius with diameter, using the area formula when circumference is requested, or failing to leave answers in terms of pi or round the shaded-sector area as directed. Students may also confuse arc measures with sector area, misidentify a tangent or point of tangency, or match chord, secant, radius, and diameter labels incorrectly. In the tangent problems, check that they use the right-angle relationship and interpret the diagram before solving for a length.

How do I assign and grade the Circle Tangents worksheet?

The Circle Tangents worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key for the multiple-choice, fill-in-the-blank, and matching items, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support instruction when your school is reducing screen time.

How can I differentiate this Circle Tangents worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the circle diagrams, multiple-choice options, and matching labels are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when that better supports students working with the circle-geometry vocabulary.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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