Est. 1998 — 27 years of woodworking knowledge
Friday puzzler --Squares
Alex Y
Square A is inscribed in a circle.
Square B is inside the same circle, with one side lying along a side of A, and two corners being on the circle. (The interior of B is outside of A but inside the circle. )
What is the ratio of the area of A to the area of B?
Re: Friday puzzler --Squares
Larry Barrett
It is interesting that the ratio of these two squares can be expressed as the ratio of two perfect squares.
I believe you've got it! ;-
Alex Y
Assuming your answer is also that the ratio is a perfect square. Squares everywhere you look!
Re: I believe you've got it! ;-
Larry Barrett
yes.
The second step in the solution (and almost the final step) is to solve this equation:
2b^2 = a^2 + (2a + b)^2.
The first step is to discover why this is the second step.