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. 21​s(3​+4)
B. 21​s3​
C. 21​s(1+3​)
D. 21​s(3​−1)
E. 21​s(2−3​)
Solution:
Triangle ABX is equilateral with altitude 21​s3​. The required distance is s−21​s3​ or 21​s(2−3​).