Inscribing a Square within a Half-CircleDate: 04/05/2002 at 02:21:55 From: Michael Wright Subject: Inscribing a square within a half-circle Hello, I was wondering if there was a way to inscribe a square within a given half-circle. I have tried a few ways, e.g. using midpoints of the diameter of the circle and constructing perpendiculars, but nothing seems to work. I'm hoping you can help me with this matter. Thank you, Michael Date: 04/05/2002 at 03:52:53 From: Doctor Floor Subject: Re: Inscribing a square within a half-circle Hi, Michael, Thanks for your question. Start with the center C of the semicircle. From there draw a radius perpendicular to the bounding diameter DB. Now lines from C to the two vertices on the arc part of the semicircle must have slopes 2 and -2 respectively if we consider DB to be the x-axis. So we choose a point E on the perpendicular radius ("y-axis"), and make a square with side CE, and add a second congruent square at the top of the first. In the figure line CK has slope -2, and meets the arc in L. Now L is one of the vertices of the square. We drop an altitude LN to BD, and the rest is easy. If you have more questions, just write back. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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