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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 #21 : Circles

What is the measure of an inscribed angle with an arc measurement of $86 ^{\circ}$ $\displaystyle 86 ^{\circ}$ ?

Possible Answers:

$43\degree$ $\displaystyle 43\degree$

$87\degree$ $\displaystyle 87\degree$

$344\degree$ $\displaystyle 344\degree$

$86\degree$ $\displaystyle 86\degree$

$172\degree$ $\displaystyle 172\degree$

Correct answer:

$43\degree$ $\displaystyle 43\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=86 \cdot \frac{1}{2} \\\\=43$ $\displaystyle \\=86 \cdot \frac{1}{2} \\\\=43$

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Example Question #22 : Circles

What is the measure of an inscribed angle with an arc measurement of $54 ^{\circ}$ $\displaystyle 54 ^{\circ}$ ?

Possible Answers:

$108\degree$ $\displaystyle 108\degree$

$54\degree$ $\displaystyle 54\degree$

$55\degree$ $\displaystyle 55\degree$

$216\degree$ $\displaystyle 216\degree$

$27\degree$ $\displaystyle 27\degree$

Correct answer:

$27\degree$ $\displaystyle 27\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=54 \cdot \frac{1}{2} \\\\=27$ $\displaystyle \\=54 \cdot \frac{1}{2} \\\\=27$

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Example Question #21 : Circles

What is the measure of an inscribed angle with an arc measurement of $13 ^{\circ}$ $\displaystyle 13 ^{\circ}$ ?

Possible Answers:

$14\degree$ $\displaystyle 14\degree$

$13\degree$ $\displaystyle 13\degree$

$\frac{13}{2}\degree$ $\displaystyle \frac{13}{2}\degree$

$26\degree$ $\displaystyle 26\degree$

$52\degree$ $\displaystyle 52\degree$

Correct answer:

$\frac{13}{2}\degree$ $\displaystyle \frac{13}{2}\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=13 \cdot \frac{1}{2} \\\\=\frac{13}{2}$ $\displaystyle \\=13 \cdot \frac{1}{2} \\\\=\frac{13}{2}$

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Example Question #22 : Circles

What is the measure of an inscribed angle with an arc measurement of $31 ^{\circ}$ $\displaystyle 31 ^{\circ}$ ?

Possible Answers:

$31\degree$ $\displaystyle 31\degree$

$\frac{31}{2}\degree$ $\displaystyle \frac{31}{2}\degree$

$124\degree$ $\displaystyle 124\degree$

$32\degree$ $\displaystyle 32\degree$

$62\degree$ $\displaystyle 62\degree$

Correct answer:

$\frac{31}{2}\degree$ $\displaystyle \frac{31}{2}\degree$

Explanation:

The inscribed angle is simply half the arc measurement.

$\\=31 \cdot \frac{1}{2} \\\\=\frac{31}{2}$ $\displaystyle \\=31 \cdot \frac{1}{2} \\\\=\frac{31}{2}$

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Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ , and $\displaystyle y$ .

Plot2

Possible Answers:

$\displaystyle y = 280.0 , x = 291.0$

$\displaystyle y = 260.0 , x = 249.0$

$\displaystyle y = 111.0 , x = 100.0$

$\displaystyle y = 100.0 , x = 111.0$

$\displaystyle y = 80.0 , x = 69.0$

Correct answer:

$\displaystyle y = 100.0 , x = 111.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot2

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ , and $\displaystyle y$ .

$\\180 = y + 80.0 \\180 = x + 69.0$ $\displaystyle \\180 = y + 80.0 \\180 = x + 69.0$

Now let's solve for $\displaystyle x$ , and $\displaystyle y$ .

$\\180 -80.0= y + 80.0{\color{Red} -80.0} \\180-69.0 = x + 69.0{\color{Red} -69.0}$ $\displaystyle \\180 -80.0= y + 80.0{\color{Red} -80.0} \\180-69.0 = x + 69.0{\color{Red} -69.0}$

$\\y = 100.0 \\x = 111.0$ $\displaystyle \\y = 100.0 \\x = 111.0$

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Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ and $\displaystyle y$ .

Plot3

Possible Answers:

$\displaystyle y = 88.0 , x = 131.0$

$\displaystyle y = 92.0 , x = 49.0$

$\displaystyle y = 272.0 , x = 229.0$

$\displaystyle y = 131.0 , x = 88.0$

$\displaystyle y = 268.0 , x = 311.0$

Correct answer:

$\displaystyle y = 88.0 , x = 131.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot3

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180 = y + 92.0 \\180 = x + 49.0$ $\displaystyle \\180 = y + 92.0 \\180 = x + 49.0$

Now let's solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180-92.0 = y + 92.0{\color{Red} -92.0} \\180-49.0 = x + 49.0{\color{Red} -49.0}$ $\displaystyle \\180-92.0 = y + 92.0{\color{Red} -92.0} \\180-49.0 = x + 49.0{\color{Red} -49.0}$

$\\y = 88.0 \\x = 131.0$ $\displaystyle \\y = 88.0 \\x = 131.0$

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Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ and $\displaystyle y$ .

Plot4

Possible Answers:

$\displaystyle y = 243.0 , x = 274.0$

$\displaystyle y = 94.0 , x = 63.0$

$\displaystyle y = 63.0 , x = 94.0$

$\displaystyle y = 297.0 , x = 266.0$

$\displaystyle y = 117.0 , x = 86.0$

Correct answer:

$\displaystyle y = 63.0 , x = 94.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot4

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180 = y + 117.0 \\180 = x + 86.0$ $\displaystyle \\180 = y + 117.0 \\180 = x + 86.0$

Now let's solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180-117.0 = y + 117.0{\color{Red} -117.0} \\180-86.0 = x + 86.0{\color{Red} -86.0}$ $\displaystyle \\180-117.0 = y + 117.0{\color{Red} -117.0} \\180-86.0 = x + 86.0{\color{Red} -86.0}$

$\\y = 63.0 \\x = 94.0$ $\displaystyle \\y = 63.0 \\x = 94.0$

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Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ and $\displaystyle y$ .

Plot5

Possible Answers:

$\displaystyle y = 108.0 , x = 85.0$

$\displaystyle y = 85.0 , x = 108.0$

$\displaystyle y = 252.0 , x = 275.0$

$\displaystyle y = 288.0 , x = 265.0$

$\displaystyle y = 72.0 , x = 95.0$

Correct answer:

$\displaystyle y = 108.0 , x = 85.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot5

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180 = y + 72.0 \\180 = x + 95.0$ $\displaystyle \\180 = y + 72.0 \\180 = x + 95.0$

Now let's solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180 -72.0= y + 72.0{\color{Red} -72.0} \\180 -95.0= x + 95.0{\color{Red} -95.0}$ $\displaystyle \\180 -72.0= y + 72.0{\color{Red} -72.0} \\180 -95.0= x + 95.0{\color{Red} -95.0}$

$\\y = 108.0 \\x = 85.0$ $\displaystyle \\y = 108.0 \\x = 85.0$

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Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ and $\displaystyle y$ .

Plot6

Possible Answers:

$\displaystyle y = 69.0 , x = 72.0$

$\displaystyle y = 291.0 , x = 288.0$

$\displaystyle y = 249.0 , x = 252.0$

$\displaystyle y = 108.0 , x = 111.0$

$\displaystyle y = 111.0 , x = 108.0$

Correct answer:

$\displaystyle y = 111.0 , x = 108.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot6

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180 = y + 69.0 \\180 = x + 72.0$ $\displaystyle \\180 = y + 69.0 \\180 = x + 72.0$

Now let's solve for $\displaystyle x$ and $\displaystyle y$ .

$\\180-69.0 = y + 69.0{\color{Red} -69.0} \\180-72.0 = x + 72.0{\color{Red} -72.0} \\y = 111.0 \\x = 108.0$ $\displaystyle \\180-69.0 = y + 69.0{\color{Red} -69.0} \\180-72.0 = x + 72.0{\color{Red} -72.0} \\y = 111.0 \\x = 108.0$

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Example Question #3 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

From the following picture, determine $\displaystyle x$ , and $\displaystyle y$ .

Plot7

Possible Answers:

$\displaystyle y = 254.0 , x = 252.0$

$\displaystyle y = 108.0 , x = 106.0$

$\displaystyle y = 106.0 , x = 108.0$

$\displaystyle y = 286.0 , x = 288.0$

$\displaystyle y = 74.0 , x = 72.0$

Correct answer:

$\displaystyle y = 106.0 , x = 108.0$

Explanation:

Since this polygon is inscribed within a circle, we know a few things.

Plot7

The first thing we know is that the sum of all the interior angles must equal $360^{\circ}$ $\displaystyle 360^{\circ}$ .

The last thing we know, the most important one is all opposite angles must equal $180^{\circ}$ $\displaystyle 180^{\circ}$ .

Now we need to set up equations to solve for $\displaystyle x$ , and $\displaystyle y$ .

$\\180 = y + 74.0 \\180 = x + 72.0$ $\displaystyle \\180 = y + 74.0 \\180 = x + 72.0$

Now let's solve for $\displaystyle x$ , and $\displaystyle y$ .

$\\180 -74.0= y + 74.0{\color{Red} -74.0} \\180 -72.0= x + 72.0{\color{Red} -72.0} \\y = 106.0 \\x = 108.0$ $\displaystyle \\180 -74.0= y + 74.0{\color{Red} -74.0} \\180 -72.0= x + 72.0{\color{Red} -72.0} \\y = 106.0 \\x = 108.0$

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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 #21 : Circles

Example Question #22 : Circles

Example Question #21 : Circles

Example Question #22 : Circles

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #1 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #2 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

Example Question #3 : Inscribed And Circumscribed Circle Of Triangles: Ccss.Math.Content.Hsg C.A.3

All Common Core: High School - Geometry Resources

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