Concyclic pts

Is there any quick method of finding if 4 given pts are concyclic or not? (finding the eqn of the circle thru 3 pts and then checking the 4th pt in the eqn is really looooooooooong)

3 Answers

62
Lokesh Verma ·

if ABCD are the point

<ACB=<ADC

Chord subtends equal angle
then they are concyclic!

341
Hari Shankar ·

Ptolemy's theorem - maybe easy since only distances are involved

http://www.cut-the-knot.org/proofs/ptolemy.shtml

62
Lokesh Verma ·

yes this too..

it was my most favorite theorem in Geometry ptolmey's

Your Answer

Close [X]