Question

If A,B,C,D are four consecutive points on a circle such that AB = CD, then show that
AC = BD

Answer 1

Answer:

Form a square in it and then relation will be satisfied

Step-by-step explanation:

Answer 2

Answer:

Draw circle O and mark points A & B on it (I suggest such that central angle AOB is around 30 to 60 degrees.

Elsewhere, marks points C & D on the circle with central angle COD equaling angle COD.  The arrangement of points on the circle will be such that you go from A to B to C to D by moving clockwise around the circle.

 

Then equal chords AB & CD have equal arcs AB & CD.

 

Note that arc ABC will equal arc BCD, because arc AB + arc BC = arc BC + arc CD.

 

The chords of arc ABC & arc BCD will therefore be equal ("equal arcs have equal chords, on a given circle").

 

Therefore AC = BD.

Step-by-step explanation:

Hope it helps