CBSE Class 9 Answered

let AB,CD be the intersecting chords intersecting at E.

P be the point of intersection and O be the center of the circle, obviously O lies on the diameter.

draw OL and OM perpendiculars to AB,CD respectively.

in triangles LOP,MOP,

we have

angle LPO=angle MPO.... given

angle OMP= angle OLP.. each 90 degrees because of construction

OP=OP....common

so triangles become congruent

so

OL=OM... CPCT

thus we can say,

distance of AB from the center = dist of CD from the center

so

AB=CD

 chords which are equidistant from the center are equal in length.