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Common Core: High School - Geometry : Circles

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Circles

Given $\frac{C}{C'}=25$ $\displaystyle \frac{C}{C'}=25$, and R=4 $\displaystyle R=4$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=25 $\displaystyle R'=25$

R'=4 $\displaystyle R'=4$

$R'=\frac{4}{25}$ $\displaystyle R'=\frac{4}{25}$

R'=100 $\displaystyle R'=100$

$R'=\frac{25}{4}$ $\displaystyle R'=\frac{25}{4}$

Correct answer:

$R'=\frac{4}{25}$ $\displaystyle R'=\frac{4}{25}$

Explanation:

In order to do this problem, we need to remember the relationship between Circumference's, and Radii. $\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$. With this relationship, we can determine what $\displaystyle R'$ is.

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$25=\frac{4}{R'}$ $\displaystyle 25=\frac{4}{R'}$

Multiply by $\displaystyle R'$ on each side.

25R'=4 $\displaystyle 25R'=4$

Divide by $\displaystyle 25$ to get $\displaystyle R'$.

$R'=\frac{4}{25}$ $\displaystyle R'=\frac{4}{25}$

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Example Question #1 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Given $\frac{C}{C'}=118$ $\displaystyle \frac{C}{C'}=118$, and R=12 $\displaystyle R=12$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=6 $\displaystyle R'=6$

$R'=\frac{6}{59}$ $\displaystyle R'=\frac{6}{59}$

R'=118 $\displaystyle R'=118$

$R'=\frac{1}{118}$ $\displaystyle R'=\frac{1}{118}$

R'=59 $\displaystyle R'=59$

Correct answer:

$R'=\frac{6}{59}$ $\displaystyle R'=\frac{6}{59}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$118=\frac{12}{R'}$ $\displaystyle 118=\frac{12}{R'}$

Multiply by $\displaystyle R'$ on each side.

$\displaystyle 118R'=12$

Divide by 118 $\displaystyle 118$ to get $\displaystyle R'$.

$R'=\frac{12}{118}=\frac{6}{59}$ $\displaystyle R'=\frac{12}{118}=\frac{6}{59}$

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Example Question #2 : Circles

Given $\frac{C}{C'}=115$ $\displaystyle \frac{C}{C'}=115$, and R=9 $\displaystyle R=9$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

$R'=\frac{9}{115}$ $\displaystyle R'=\frac{9}{115}$

$R'=\frac{115}{9}$ $\displaystyle R'=\frac{115}{9}$

R'=106 $\displaystyle R'=106$

R'=9 $\displaystyle R'=9$

R'=115 $\displaystyle R'=115$

Correct answer:

$R'=\frac{9}{115}$ $\displaystyle R'=\frac{9}{115}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$115=\frac{9}{R'}$ $\displaystyle 115=\frac{9}{R'}$

Multiply by $\displaystyle R'$ on each side.

115R'=9 $\displaystyle 115R'=9$

Divide by 115 $\displaystyle 115$ to get $\displaystyle R'$.

$R'=\frac{9}{115}$ $\displaystyle R'=\frac{9}{115}$

Report an Error

Example Question #3 : Circles

Given $\frac{C}{C'}=58$ $\displaystyle \frac{C}{C'}=58$, and R=6 $\displaystyle R=6$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

$R'=\frac{29}{3}$ $\displaystyle R'=\frac{29}{3}$

R'=58 $\displaystyle R'=58$

R'=29 $\displaystyle R'=29$

R'=3 $\displaystyle R'=3$

$R'=\frac{3}{29}$ $\displaystyle R'=\frac{3}{29}$

Correct answer:

$R'=\frac{3}{29}$ $\displaystyle R'=\frac{3}{29}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$58=\frac{6}{R'}$ $\displaystyle 58=\frac{6}{R'}$

Multiply by $\displaystyle R'$ on each side.

58R'=6 $\displaystyle 58R'=6$

Divide by $\displaystyle 58$ to get $\displaystyle R'$.

$R'=\frac{6}{58}=\frac{3}{29}$ $\displaystyle R'=\frac{6}{58}=\frac{3}{29}$

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Example Question #4 : Circles

Given $\frac{C}{C'}=55$ $\displaystyle \frac{C}{C'}=55$, and R=18 $\displaystyle R=18$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=18 $\displaystyle R'=18$

$R'=\frac{18}{55}$ $\displaystyle R'=\frac{18}{55}$

$R'=\frac{1}{18}$ $\displaystyle R'=\frac{1}{18}$

R'=55 $\displaystyle R'=55$

$R'=\frac{55}{18}$ $\displaystyle R'=\frac{55}{18}$

Correct answer:

$R'=\frac{18}{55}$ $\displaystyle R'=\frac{18}{55}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$55=\frac{18}{R'}$ $\displaystyle 55=\frac{18}{R'}$

Multiply by $\displaystyle R'$ on each side.

55R'=18 $\displaystyle 55R'=18$

Divide by $\displaystyle 55$ to get $\displaystyle R'$.

$R'=\frac{18}{55}$ $\displaystyle R'=\frac{18}{55}$

Report an Error

Example Question #3 : Circles

Given $\frac{C}{C'}=113$ $\displaystyle \frac{C}{C'}=113$, and R=12 $\displaystyle R=12$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=113 $\displaystyle R'=113$

$R'=\frac{12}{113}$ $\displaystyle R'=\frac{12}{113}$

$R'=\frac{1}{12}$ $\displaystyle R'=\frac{1}{12}$

$R'=\frac{113}{12}$ $\displaystyle R'=\frac{113}{12}$

R'=12 $\displaystyle R'=12$

Correct answer:

$R'=\frac{12}{113}$ $\displaystyle R'=\frac{12}{113}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$113=\frac{12}{R'}$ $\displaystyle 113=\frac{12}{R'}$

Multiply by $\displaystyle R'$ on each side.

$\displaystyle 113R'=12$

Divide by 113 $\displaystyle 113$ to get $\displaystyle R'$.

$R'=\frac{12}{113}$ $\displaystyle R'=\frac{12}{113}$

Report an Error

Example Question #1 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Given $\frac{C}{C'}=113$ $\displaystyle \frac{C}{C'}=113$, and R=16 $\displaystyle R=16$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=113 $\displaystyle R'=113$

R'=16 $\displaystyle R'=16$

$R'=\frac{113}{16}$ $\displaystyle R'=\frac{113}{16}$

$R'=\frac{1}{16}$ $\displaystyle R'=\frac{1}{16}$

$R'=\frac{16}{113}$ $\displaystyle R'=\frac{16}{113}$

Correct answer:

$R'=\frac{16}{113}$ $\displaystyle R'=\frac{16}{113}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$113=\frac{16}{R'}$ $\displaystyle 113=\frac{16}{R'}$

Multiply by $\displaystyle R'$ on each side.

$\displaystyle 113R'=16$

Divide by 113 $\displaystyle 113$ to get $\displaystyle R'$.

$R'=\frac{16}{113}$ $\displaystyle R'=\frac{16}{113}$

Report an Error

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Given $\frac{C}{C'}=36$ $\displaystyle \frac{C}{C'}=36$, and R=8 $\displaystyle R=8$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=2 $\displaystyle R'=2$

R'=9 $\displaystyle R'=9$

$R'=\frac{9}{2}$ $\displaystyle R'=\frac{9}{2}$

$R'=\frac{2}{9}$ $\displaystyle R'=\frac{2}{9}$

R'=36 $\displaystyle R'=36$

Correct answer:

$R'=\frac{2}{9}$ $\displaystyle R'=\frac{2}{9}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$36=\frac{8}{R'}$ $\displaystyle 36=\frac{8}{R'}$

Multiply by $\displaystyle R'$ on each side.

36R'=8 $\displaystyle 36R'=8$

Divide by $\displaystyle 36$ to get $\displaystyle R'$.

$R'=\frac{8}{36}=\frac{2}{9}$ $\displaystyle R'=\frac{8}{36}=\frac{2}{9}$

Report an Error

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Given $\frac{C}{C'}=92$ $\displaystyle \frac{C}{C'}=92$, and R=5 $\displaystyle R=5$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

$R'=\frac{1}{92}$ $\displaystyle R'=\frac{1}{92}$

$R'=\frac{92}{5}$ $\displaystyle R'=\frac{92}{5}$

R'=5 $\displaystyle R'=5$

R'=92 $\displaystyle R'=92$

$R'=\frac{5}{92}$ $\displaystyle R'=\frac{5}{92}$

Correct answer:

$R'=\frac{5}{92}$ $\displaystyle R'=\frac{5}{92}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$92=\frac{5}{R'}$ $\displaystyle 92=\frac{5}{R'}$

Multiply by $\displaystyle R'$ on each side.

92R'=5 $\displaystyle 92R'=5$

Divide by $\displaystyle 92$ to get $\displaystyle R'$.

$R'=\frac{5}{92}$ $\displaystyle R'=\frac{5}{92}$

Report an Error

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Given $\frac{C}{C'}=76$ $\displaystyle \frac{C}{C'}=76$, and R=6 $\displaystyle R=6$, what is R'? $\displaystyle R'?$

Screen shot 2020 07 01 at 7.06.26 pm

Possible Answers:

R'=38 $\displaystyle R'=38$

$R'=\frac{3}{38}$ $\displaystyle R'=\frac{3}{38}$

$R'=\frac{38}{3}$ $\displaystyle R'=\frac{38}{3}$

$R'=\frac{1}{38}$ $\displaystyle R'=\frac{1}{38}$

R'=3 $\displaystyle R'=3$

Correct answer:

$R'=\frac{3}{38}$ $\displaystyle R'=\frac{3}{38}$

Explanation:

$\frac{C}{C'}=\frac{R}{R'}$ $\displaystyle \frac{C}{C'}=\frac{R}{R'}$

Substitute for the variables given in the question.

$76=\frac{6}{R'}$ $\displaystyle 76=\frac{6}{R'}$

Multiply by $\displaystyle R'$ on each side.

76R'=6 $\displaystyle 76R'=6$

Divide by $\displaystyle 76$ to get $\displaystyle R'$.

$R'=\frac{6}{76}=\frac{3}{38}$ $\displaystyle R'=\frac{6}{76}=\frac{3}{38}$

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Circles

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Circles

Example Question #1 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Example Question #2 : Circles

Example Question #3 : Circles

Example Question #4 : Circles

Example Question #3 : Circles

Example Question #1 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

Example Question #2 : Similar Circles: Ccss.Math.Content.Hsg C.A.1

All Common Core: High School - Geometry Resources

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