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Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

Calculate a point that is tangent to the circle (x-5)^2+(y-3)^2=9 and passes through the origin.

(5,0)

(3,0)

(0,3)

(0,5)

(3,2)

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Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

Calculate a point that is tangent to the circle (x-5)^2+(y-3)^2=9 and passes through the origin.

Your answer:

(3,0)

Your answer:

(0,3)

Your answer:

(0,5)

Your answer:

(3,2)

Correct answer:

(5,0)

Explanation:

To construct a line that is tangent to a point on the circle and passes through the origin, 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,

(x-5)^2+(y-3)^2=9

the center and radius of the circle can be determined.

(x-h)^2+(y-k)^2=r^2

The center is located at (h,k) and the radius is .

Therefore, the center is located at (5,3) and the radius is three. Plotting the circle and tangent line to the origin results in the following.

Screen shot 2016 07 14 at 10.07.14 am

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All Common Core: High School - Geometry Resources

Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

Flashcards: Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4

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