Question

Show that if two chords of a circle bisect one another they must be diameters.

Answer 1

Given-> 2 chords AB and CD
O is midpoint of AB and CD
To prove->AB and CD are diameter
Proof->`/_AOC and /_BOD`
`/_AOC=/_BOD`
`OA=OB`
`OC=OD`
`/_AOC cong /_BOD(SAS)`
`AC=BD-(1)`
`In /_AOD and /_BOC`
`/_AOD=/_BOC`
`OA=OB`
`OC=OD`
`/_AOD cong /_BOC(SAS)`
`AD=BC-(2)`
adding equation 1 and 2
`AC+AD=BC+BD`
`CAD=CBD`
CD is diameter of circle
AB is diameter of circle.