Question

Please help. 10 points. Please do not guess. Guesses will be reported. Thank you. :)

Answer 1

a. The radius is the distance from the circle's center to the point of tangency:

$\sqrt{(10-6)^2+(5-(-3))^2}=\sqrt{80}=4\sqrt5$

b. The line tangent to the circle is perpendicular to the line connecting points A and B. Lines perpendicular to one another have slopes that are negative reciprocals of one another. In other words, if the slope of the line through A and B is $m$, then the slope of the tangent line is $-\dfrac1m$.

Find the slope of the line through A and B:

$m=\dfrac{10-6}{5-(-3)}=\dfrac12\implies-\dfrac1m=-2$