Question

A square ABCD of unit side is drawn along with a circle C1 of unit radius centered at A. Another circle C2 is drawn such that it touches C1 and AB and AD being tangents to it. If a tangent at C2 from point C touches the side AB at E then the length of EB is x+y(3)^(1/2) then x+y=?​

Answer 1

Answer:

Answer

Let   be the centers and the radii of the circles . Let  be the points of tangency from the common external tangent of , respectively, and let the extension of  intersect the extension of at a point . Let the endpoints of the chord/tangent be  and the foot of the perpendicular from to be . From the similar right triangles

It follows that , and that 

By the Pythagorean Theorem on  we find that

and the answer is m+n+p=405