Question

Two different circles that pass through the point (1,3) are tangent to both coordinate axes. If the length of the radius of the smaller circle is "r" and the length of the radius of the larger circle is "R", what is the value of "r+R"?

Answer 1

ok,
since both circles share the same point, they can be represented by the equation
(1-a)^2+(3-a)^2=a^2
where a=r or R

Answer 2

note that I am using the equation of the circle

Answer 3

expand that out and you get:
a^2-8a+10=0

Answer 4

solve for a, and you get 4-rt6 and 4+rt6
where r=4-rt6 and R=4+rt6

Answer 5

and them both and you get a total of 8

Answer 6

ok