Big Circles vs. Small Circle

if we draw the triangle we come an equation using phytagorean theorem; (r + 4)^2 = (r - 4)^2 + 4^2 if simplify the equation then we get; r = 1

according to the given diagram the big circle radius is 4 as AD is 8. through geometry the small circle is exactly half the radius of the bigger circle means diameter 2 thus, r is 1.

let the radius of small circle be r since, the diameter is 8cm (breadth = diameter (from the figure)) by making triangle with (H)hypotan.=rad of big cir(R) + rad of small circle(r)=4+r and (P)perpendicular =half of breadth(b) - r=4-r and by diagram base(B)=4cm by pythagoras theorem ,we get H^2=P^2+B^2 (4+r)^2=(4-r)^2+4^2 on solving this equation,we get r=1

The big circle has a radius of 2 cm as AD is 8. And the small circle is exactly half the radius of the bigger circle means diameter 2 thus, r is 1.

r=1