If a, b ( b is greaterthan a) be the diameters of two concentric circles and 'c' be the length of a chord of a circle which is tangent to the other circle, then find the value of b in terms of a and c.

Answer 1

did you make a sketch?
Draw a common diameter.
The radius of the larger circle will be b/2, and that of the smaller circle is a/2
draw the tangent so that it hits the end of the diameter.
you will have a right-angled triangle, so that
(b/2)^2 = (c/2)^2 + (a/2)^2
b^2 /4 = c^2/4 + a^2/4
b^2 = c^2 + a^2 <----- that should do it

or

b = √(c^2 + a^2)