SOLUTION: Two circles are internally tangent. The smaller circle is also tangent to two perpendicular radii of the larger circle. What is the ratio of the area of the small circle to the are

Algebra ->  Triangles -> SOLUTION: Two circles are internally tangent. The smaller circle is also tangent to two perpendicular radii of the larger circle. What is the ratio of the area of the small circle to the are      Log On


   

Question 1175959: Two circles are internally tangent. The smaller circle is also tangent to two perpendicular radii of the larger circle. What is the ratio of the area of the small circle to the area of the large circle. Express your answer is simplest radical form.
My answer - π. There is no integer given, so I am guessing that it should be π. Please correct me.
No diagram given
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
Let the radius of the largest circle is 2 and the radius of the smaller circle be r.

You can write an expression to find r:

r+%2B+r+%2A+sqrt%282%29+=+2
r+=+2%2F%281%2Bsqrt%282%29%29

r+=+2sqrt%282%29+-+2

So, the ratio of the areas is %282sqrt%282%29+-+2%29%2F%284%29+=+%28sqrt%282%29-1%29%2F2