Problem: Inside square ABCD with side s, quarter-circle arcs with radii s and centers at A and B are drawn. These arcs intersect at a point X inside the square. How far is X from side CD?
Answer Choices:
A. 21s(3+4)
B. 21s3
C. 21s(1+3)
D. 21s(3−1)
E. 21s(2−3)
Solution:
Triangle ABX is equilateral with altitude 21s3. The required distance is s−21s3 or 21s(2−3).