BE and CD are two equal chords of circle with centre O. These chords when produced meet at E. Prove that BE = ED .

Asked by Vikas | 11th Jan, 2018, 09:10: AM

Expert Answer:

 
begin mathsize 16px style Construction colon space Join space OE. space Draw space OL perpendicular AB space and space OM perpendicular CD
AB equals CD
rightwards double arrow OL equals OM space space space space left parenthesis Equal space chords space are space equidistant space from space the space centre right parenthesis
In space triangle OLE space and space triangle OME comma
OL equals OM
angle OLE equals angle OME
OE equals OE space space space space space left parenthesis Each equals 90 degree right parenthesis
rightwards double arrow triangle OLE approximately equal to triangle OME space space space space left parenthesis By space RHS space congruence right parenthesis
rightwards double arrow EL equals EM space space space space space.... left parenthesis straight i right parenthesis
Now comma space AB equals CD
rightwards double arrow 1 half AB equals 1 half CD
rightwards double arrow BL equals DM space space space space space space.... left parenthesis ii right parenthesis
left parenthesis straight i right parenthesis minus left parenthesis ii right parenthesis
EL minus BL equals EM minus DM
rightwards double arrow BE equals DE end style

Answered by Rashmi Khot | 11th Jan, 2018, 10:24: AM