please help ive look at this question for hours and got no where. find the radii of the 2 circles which have their centre at the origin and which touch the circle x^2 + y^2 - 8x - 6y + 21 = 0 ??

Question

thanks for the help

Answer 1

by completing the square I go
(x-4)^2 + (y-3)^2 = 4
The circle has centre (4,3) and radius 2
Sketch it
Now draw 2 circles with centre at the origin, one to touch the given circle on the outside and one to touch it on the inside.
The line from the origin through (4,3) will run through the points where the circles touch.
By Pythagoras the distance from (0,0) to (4,3) is 5
Since the radius of the given circle is 2,
the radius of the smaller circle at the origin has to be 3, and the radius of the larger circle has to be 7

Answer 2

thanks so much