The diagram below shows four congruent circles whose centres are the vertices of the square DEFG and whose circumference touch the sides of an isosceles triangle. Area of triangle ABC is 10000 units square. What is the radius of the circles, to the nearest unit.
The Attempt at a Solution
Let the sides AB=BC=x and the radius, r.
1/2 x^2=10000 so x is approximately 142
AC = 141 sqrt(2)
I assumed that the height of the triangle ABC passes through BEG and the point where the bottom circle touches AC. Maybe this is why i arrived at the wrong answer.
(1/2)(r) (141 sqrt(2))(1+sqrt(8)+sqrt(2))=10000
But the answer given is 19.