Q. 224.2( 5 Votes )

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points, without finding the center of the circle. Justify the construction.

Answer :

Let A, B, C, D be the given points.


With B as center and radius equal to AC draw an arc.


With C as center and AB as radius draw another arc.


Which cuts the previous arc at D,


Then, D is the required point BD and CD.



In ΔABC and ΔDCB,


AB = DC


AC = DB


BC = CB


ΔEBC ΔEDA


BAC = CDB


Thus, BC subtends equal angles, BAC and CDB on the same side of it.


Therefore, points A, B, C, D are concyclic.


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