Question

A,b,c and d qre four points on a circle such that ab= cd . Prove that ac= bd

Answer 1

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.