How do you find x coordinate?

Question

A circle C1 of radius 5 has its center at the origin. Inside this circle, there is a first quadrant circle C2 of radius 2 that is tangent to C1. The y coordinate of the center of C2 is 2. Find x coordinate of the center of C2.

The answer is sqrt of 5. How do you get it?Thanks

Answer 1

if the two circles are tangential then the centers and the point of intersection are collinear.

the distance from the center of the circle C1 to the center of the circle C2 is thus 3 units. Since the radius of C1 is 5 and the radius of C2 = 2 .. . .

(x - 0)^2 + (2 - 0)^2 = 9

x^2 = 9 - 4 = 5

thus

x = √5 (since the circle C2 is in the first quadrant)

Answer 2

the  radius is 5 of C! and C2 is tangent on C1.

hence the on rt angle triangle basis

x^2+2^2 = 3^2  i.e ( C1radius _ C2 radius)

hence x = sqrt 5

ans