[net.puzzle] Solution to triangles in a square

vasudev@asgb.UUCP (08/13/84)

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