Construct X^2 using compass and straight edge

Question From Vijayan Sir
Given a right triangle with 'unit length' base and 'x unit' height. construct X^2 using compass and straight edge?
------------------------
Answer Given by KANI

kani December 29, 2010 10:00 PM

Let ABC be right traingle with Angle A=90,AB=1&AC=x
1. Elongate BA
2. Draw perpendicular bisector of BC to intersect elongated line at O.
3. Find a point D on the same elongated line such that OD=OB

Then AD= x^2
----------------
If x=2, x^2=4
See the picture.

If x=3, x^2=9
See the picture.

To be added:
This question can be interpreted in anotherway using co-ordinate geometry.

See fig.
Elongate CA and consider these perpendiculars BD and CA as X,Y axes respectively.
Take B as 1 and C as x.
Then D is x^2.
Here D can be obtained directly as the point of intersection of X axis and the perpendiculr to BC through C.