Question

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

Answer 1

Answer is B) 10 units

hope that helps

Answer 2

we know that

if the line segment KL is tangent to circle J at point K

then

KL is perpendicular to KJ

the triangle KJL is a right triangle

Applying the Pythagorean Theorem

$LJ^{2} =KL^{2}+KJ^{2}$

we have

$KL=24\ units\\KJ=r\ units\\JL=(16+r)\ units$

substitute the values

$(16+r)^{2} =24^{2}+r^{2}\\256+32r+ r^{2}=576+ r^{2} \\32r=576-256 \\r= 320/32\\r=10\ units$

therefore

the answer is the option B

$10\ units$