SAT Math Multiple Choice Practice Question 507: Answer and Explanation
In the figure above, A and B are the centers of two circles of identical circumference. is tangent to both circles and parallel to (not shown). If r is the radius of the circle with center A, what is the area of quadrilateral ABCD (not shown) in terms of r ?
Correct Answer: E
E Because A is the center of one circle and B is a point on the circumference, is r. and are also r. Whenever a line is tangent to a circle, the radius drawn to the point of tangency is perpendicular to the line. So, and are perpendicular to . That means ABCD is a square. Plug in for the radius, say r = 6. The area of a square is the square of a side, so the area is 36. Plug 6 into the answer choices to see which agrees with 36. Only E is 36!