In three line segments OA, OB and OC,points L,M,Nrespectively are so shosen that LM ll AB and MN ll BC but neither of L, M nor of A,B,C are collinear. Show that LN ll AC.

Asked by gpnkumar0 | 7th Mar, 2018, 09:37: PM

Expert Answer:

begin mathsize 16px style Given colon
In space three space line space segments space OA comma space OB space and space OC space points space straight L comma space straight M comma space straight N space respectively space are space so space chosen
that space LM parallel to AB space and space MN parallel to BC space
Neither space of space straight L comma space straight M comma space straight N space nor space of space straight A comma space straight B comma space straight C space are space collinear.
To space prove colon space LN parallel to AC
Proof colon
increment OAB comma
LM parallel to AB
OL over LA equals OM over MB.................. BPT
LA over OL equals OM over MB
LA over OL plus 1 equals OM over MB plus 1
fraction numerator LA plus OL over denominator OL end fraction equals fraction numerator OM plus MB over denominator MB end fraction
OA over OL equals OB over OM............ left parenthesis 1 right parenthesis
Similarly comma space in space increment OBC comma
MN parallel to BC
OC over ON equals OB over OM........ left parenthesis 2 right parenthesis
OA over OL equals OC over ON....... from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
In space increment OAC
LN parallel to AC....................... Converse space of space BPT end style

Answered by Sneha shidid | 8th Mar, 2018, 09:08: AM