Common Core: High School - Geometry : High School: Geometry

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

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #7 : Construct Tangent Lines From Outside A Circle: Ccss.Math.Content.Hsg C.A.4

Calculate a point that is tangent to the circle  and passes through the point .

Possible Answers:

Correct answer:

Explanation:

To construct a line that is tangent to a point on the circle and passes through the point , recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Given the equation of the circle,

the center and radius of the circle can be determined.

The center is located at  and the radius is .

Therefore, the center is located at  and the radius is three. Plotting the circle and tangent line to the point  results in the following.

Screen shot 2016 07 14 at 10.42.33 am

Therefore, the point on the circle that creates a tangent line, .

Example Question #8 : Construct Tangent Lines From Outside A Circle: Ccss.Math.Content.Hsg C.A.4

Calculate a point that is tangent to the circle  and passes through the point .

Possible Answers:

Correct answer:

Explanation:

To construct a line that is tangent to a point on the circle and passes through the point , recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Given the equation of the circle,

the center and radius of the circle can be determined.

The center is located at  and the radius is .

Therefore, the center is located at  and the radius is three. Plotting the circle and tangent line to the point  results in the following.

Screen shot 2016 07 14 at 10.53.27 am

Therefore, the point on the circle that creates a tangent line with the point given is .

Example Question #9 : Construct Tangent Lines From Outside A Circle: Ccss.Math.Content.Hsg C.A.4

 

Plot4

Construct a line that is tangent to the circle. 

Possible Answers:

Plot9.1

Plot2.1

None of the images depict a tangent line.

Plot4.1

Plot5.1

Correct answer:

Plot4.1

Explanation:

To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Using the plotted circle one possible line would touch the circle is as follows. 

Plot4.1

Thus resulting in a tangent line to the circle.

Example Question #251 : High School: Geometry

C.a.4 1

Construct a line that is tangent to a point on the circle and passes through the point .

Possible Answers:

C.a.4 1 wrong answer 2

C.a.4 3

C.a.4 1 wrong answer 3

C.a.4 1 wrong answer 1

C.a.4 1 wrong answer 4

Correct answer:

C.a.4 3

Explanation:

To construct a line that is tangent to a point on the circle and passes through the point , recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.

C.a.4 1

Constructing the first potential tangent line, a point can be plotted on the circle as follows.

C.a.4 2

From here, connect the given point  to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.

 

C.a.4 3

Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.

Example Question #252 : High School: Geometry

C.a.4 1
Construct a line that is tangent to a point on the circle and passes through the point .

Possible Answers:

 C.a.4 1 wrong answer 2

C.a.4 1 bottom line

C.a.4 1 wrong answer 4

C.a.4 1 wrong answer 3

C.a.4 1 wrong answer 1

Correct answer:

C.a.4 1 bottom line

Explanation:

To construct a line that is tangent to a point on the circle and passes through the point , recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.

C.a.4 1

Constructing the second potential tangent line, a point can be plotted on the circle as follows.

From here, connect the given point  to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.

C.a.4 1 bottom line 

Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.

Example Question #251 : High School: Geometry

Determine whether the statement is true or false.

Plot1

A tangent line to the circle can be constructed between the point at  and a point on the circle.

Possible Answers:

True

False

Correct answer:

True

Explanation:

To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.

Plot1

Constructing the tangent line results in the following image,

Plot2.1

Therefore, this statement is true.

Example Question #1 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5

If the radius is , and the central angle is  find the arc length.

Possible Answers:

Correct answer:

Explanation:

To find the arc length, we simply multiply the radius by the central angle.

Example Question #1 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5

If the radius is  , and the central angle is  find the arc length.

 

Possible Answers:

Correct answer:

Explanation:

To find the arc length, we simply multiply the radius by the central angle.

Example Question #252 : High School: Geometry

If the radius is , and the central angle is  find the arc length.

Possible Answers:

Correct answer:

Explanation:

To find the arc length, we simply multiply the radius by the central angle.

Example Question #2 : Arc Length, Radii, Radian, And Sector Similarity And Proportionality: Ccss.Math.Content.Hsg C.B.5

If the radius is , and the central angle is  find the arc length.

Possible Answers:

Correct answer:

Explanation:

To find the arc length, we simply multiply the radius by the central angle.

All Common Core: High School - Geometry Resources

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