a. The radius is the distance from the circle's center to the point of tangency:
[tex]\sqrt{(10-6)^2+(5-(-3))^2}=\sqrt{80}=4\sqrt5[/tex]
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 [tex]m[/tex], then the slope of the tangent line is [tex]-\dfrac1m[/tex].
Find the slope of the line through A and B:
[tex]m=\dfrac{10-6}{5-(-3)}=\dfrac12\implies-\dfrac1m=-2[/tex]
