The two circles in the figure are congruent and have their centers on the line . They are tangent to each other and to the square . The radius of the circles is . Calculate the area of the square .

Source: NCTM Mathematics Teacher, December 2005

**SOLUTION**

**
** is tangent to the left circle at point and the secant segment intersects the circle at points and

Using the quadratic formula

Triangle is a triangle with side

Area of square

**Answer**: square units

**Alternative solution
**

Triangle is a triangle with hypotenuse

Area of square

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