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Based on the tangent theorem and Pythagorean theorem, the length of the radius of the circle is: r = 85/12.

What is the Tangent Theorem?

The tangent theorem states that if a line is tangent to a circle, it is perpendicular to the radius of the circle, and therefore, angle 90 is formed at the point of tangency.

Thus:

ΔJKL is a right triangle based on the tangent theorem.

Therefore, apply Pythagorean theorem:

(6 + r)² = 11² + r²

(6 + r)(6 + r) = 121 + r²

36 + 12r + r² = 121 + r²

Combine like terms

36 - 121 = - 12r

-85 = -12r

r = 85/12

Therefore, based on the tangent theorem and Pythagorean theorem, the length of the radius of the circle is: r = 85/12.

Learn more about the tangent theorem on:

https://brainly.com/question/9892082

The length of the radius of the circle is; 85/12

What is the Tangent Theorem?

The tangent theorem is a circle theorem that states a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

From our given diagram, we can say that;

ΔJKL is a right angle triangle using the tangent theorem.

Finally, using Pythagoras theorem;

(6 + r)² = 11² + r²

(6 + r)(6 + r) = 121 + r²

36 + 12r + r² = 121 + r²

This reduces to;

12r = 121 - 36

12r = 85

radius; r = 85/12

Read more about the tangent theorem at; https://brainly.com/question/9132922

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