Answer to Question #13555 in Geometry for john

Question

B is the center of the larger circle and C is the center of the smaller circle. A is a point on the larger circle such that angles ABC form a right angled triangle, and the length of AC is 5. the bigger circle has area 9 pie. what is the perimeter of the bigger circle and the perimeter of the smaller circle?

Answer 1

Area the of largest circle is pi*r^2=9;

r^2 = 9 pi / pi;

r = 3;

So, AB = 3;

BC^2 = AC^2 - AB^2 = 25 - 9 = 16;

BC = 4;
Let O be the point of tangency of the circles with the centers B and C respectively.

BC = BO + OC;

BO = r = 3 => OC = 1;

P_big = 2*pi*BO = 6*pi;

P_small = 2*pi*C0 = 2*pi