`B M\ a n d\ C N` are perpendicular to a line passing through the vertex `A` of a triangle `A B Cdot` If `L` is the mid-point of `B C` , prove that `L M=L N`

Explanation

let l is a straight line passing through the vertex A

BM perpendicular l and CN perpendicular l

L is the mid-point of BC

Draw OL perpendicular l

If a transversal make equal intercepts on three or more parallel lines, then any other transversal intersecting them will also make equal intercepts.
BM perpendicular l and CN perpendicular l and OL perpendicular l
so `BM||OL||CN`

Now, `BM||OL||CN` and BC is the transversal making equal intercepts.

so`BL=LC`

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