【Haichuan Teahouse】Brain-teasing series: It seems complicated, but that circle is actually just a decoy
Thread Content
The side length of the large square ABCD is 8. A circle is drawn with center D and radius 4; the four vertices of the square EFHJ lie on this circle. Find the area of the shaded region. The diagrams in this question are too complex; most people don’t feel confident enough to read it through. As long as one has seen previous brain-teasing questions, it’s a verbal-answer question.
This post was last edited by Yang Qing on 2021-7-20 08:56. The radius of the circle is 4, and the side length of the square is 4√2; considering the special case where the two squares are orthogonal, the area of the shaded region is 8.
This post was last edited by Yang Qing on 2021-7-20 08:53. The area of the small square is 8 :) I mistook it; I thought the diameter was 4, but the question refers to the radius. …… Let me take another look
The circle, or the center, is necessary; without it, the small square cannot rotate. In other words, the side length of the small square needs to be determined
Rotate the small circle appropriately; when F coincides with K and H coincides with J, what needs to be calculated is the area of the triangle, which is 4*4/2=8.