Arcs Inside a SquareDate: 07/25/99 at 20:29:57 From: Susan Subject: Geometry and problem solving I can't draw this problem, so I'll explain it to you. Draw a square ABCD. Two arcs are drawn between points A and C (inside the square). Two arcs are drawn between points B and D (inside the square). If each side of the square is 5, what is area of the square-like figure (it is not a square) that is created by the intersection of the arcs in the square? Date: 07/26/99 at 14:58:19 From: Doctor Rick Subject: Re: Geometry and problem solving Hi, Susan. I think I have the correct figure. You didn't say where the center of each arc is, but I'm guessing that the 2 arcs from A to C have centers at B and D, and the 2 arcs from B to D have centers at A and C. Is this correct? Label the intersections of the arcs E, F, G, and H, so that the 4 arcs are AEFC, BFGD, CGHA, and DHEB. Put point J at the center of the square. Divide the region EFGH into 4 equal parts by drawing lines EG and FH. All you need to find now is the area of one of the 4 parts, such as EJF. Draw lines DE, DF, and DJ. You can find the area of EJF by subtracting the areas of 2 congruent triangles from the area of a sector of a circle. To do this, you will need to find the angle EDF and the length JF. See what you can do. There may be other ways to do it, but this will work. Have fun! - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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