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From: vasudev@asgb.UUCP
Newsgroups: net.puzzle
Subject: Solution to triangles in a square
Message-ID: <527@asgb.UUCP>
Date: Mon, 13-Aug-84 14:33:12 EDT
Article-I.D.: asgb.527
Posted: Mon Aug 13 14:33:12 1984
Date-Received: Wed, 15-Aug-84 06:53:00 EDT
Organization: Burroughs Corporation, San Diego
Lines: 37

Use the following result:

A triangle inscribed in a semi-circle is a right angled triangle.
The corollary to which is:
If the apex of the triangle lies outside the semi-circle then it
is an acute angled triangle.

Solution:

Let ABCD be the square.

Let E be the mid-point of AB.
Let F be the mid-point of BC.
Let G be the mid-point of CD.
Let H be the mid-point of DA.

Construct the semi-circles AH, HD
			   AB, DC
			   CF, FB
	such that they all lie in the square.

Let semi-circle AH intersect semi-circle AB at I.
Let semi-circle HD intersect semi-circle DC at J.

Join IJ.  Construct I'J' such that I'J' < IJ and is
completely within IJ.

The triangles are: AI'B, DJ'C, AI'H, HI'D, HI'J'
	and        BI'F, I'J'F and FJ'C.

Since the apexes of all the triangles lie outside
the semi-circle, they are all acute.
			
			-QED

-asgb!vasudev