Orthogonal Circles

Question

A circle of radius r is centered at the origin. A second circle is centered at (h,0) and is orthogonal to the first. Find the radius of the second circle and the abscissa of the point of intersection.

Answer 1

Radiuses to the intersection point of circles are orthogonal. So, R² + r² = h²; R = (h² - r²)^1/2; R is radius of second circle. So h > r. By properties of right triangle abscissa x of intersection point equal: x = r²/R