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marta [7]
3 years ago
10

LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that inters

ects at point K. A line is drawn from point L through a point on the circle to the center point J. The length of the radius is r, the length of K L is 11, and the length of the line segment from point L to the point on the circle is 6. What is the length of the radius? StartFraction 6 Over 85 EndFraction StartFraction 85 Over 12 EndFraction StartFraction 121 Over 36 EndFraction StartFraction 157 Over 12 EndFraction

Mathematics
2 answers:
Evgen [1.6K]3 years ago
8 0

Answer:

(B)r=\dfrac{85}{12}

Step-by-step explanation:

Given a circle centre J

Let the radius of the circle =r

LK is tangent to circle J at point K

From the diagram attached

  • LX=6
  • Radius, XJ=JK=r
  • LK=11

Theorem: The angle between a tangent and a radius is 90 degrees.

By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.

Using Pythagoras Theorem:

(6+r)^2=r^2+11^2\\(6+r)(6+r)=r^2+121\\36+6r+6r+r^2=r^2+121\\12r=121-36\\12r=85\\r=\dfrac{85}{12}

The length of the radius, r=\dfrac{85}{12}

nadezda [96]3 years ago
5 0

Answer:

The answer is B on Edge 2020

Step-by-step explanation:

I did the assignment

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