Question

Line segment KL is tangent to circle J at point K.

16
K
8
J
What is the length of the radius, r?

Answer 1

r = 12units

Explanation:

Use Phythagoras' Theorem

Hyp = (8+r)

Side A = 16

Side B = r

Hyp^2 = A^2 + B^2

(8+r)^2 = 16^2 + r^2

(8+r)(8+r) = 16r^2 + r^2

r^2 + 16r + 64 = 256 + r^2

minus r^2 on both side

16r + 64 = 256

minus 64 on both side

16r = 192

divide both side by 16

r = 192/16

r = 12 units

With this information you can also find the value of the Hyp to be 20units and the area of the Triangle to be 96units

Answer 2

The radius is of length 12.

Explanation:

A line that is tangent to a circle forms a right angle with the radius and the point of tangency. If you look closely at the diagram, you can see that a right triangle has been formed, with leg lengths r and 16 and a hypotenuse of length r + 8. Therefore, we can use the Pythagorean Theorem to find the length of the radius. I have done out the work in the attached file.

Hope this helps!