Construct a circle of radius 1. From a point on the circle, construct another............What is the area of the square?

Question

Construct a circle of radius 1. From a point on the circle, construct another circle of radius 1. Inscribe a square where the two circles overlap.
What is the area of the square?

Answer 1

Answer: ~ 0.68

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See picture below:

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Green and red lines are =1
Side of the square=x
Sides of yellow triangle ABC: AB=1, BC=x/2, AC=x+(1-x)/2=(1+x)/2
Since AB^2=BC^2+AC^2, we have 1^2=(x/2)^+((1+x)/2)^2 => x^2+1+2x+x^2=4 => 2x^2+2x-3=0 => x=1/2*(sqrt7-1) ~ 0.823
Area of square = 0.823^2 ~0.68