Associated Topics || Dr. Math Home || Search Dr. Math

### Inscribing a Square within a Half-Circle

```
Date: 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,

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/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search