Question

Consider a line AB. The line CD is drawn as the perpepndicular bisector of AB to meet AB at L. Again, EF the perpendicular bisector of AL is drawn to meet AB at M. Find the ratio of lengths of AM and AB.

Answer 1

AL is the perpendicular bisector of AB.
Clearly, AL = 0.5AB ----------- (i)
Again, AM is the perpendicular bisector of AL.
So, AM = 0.5AL ---------------- (ii)

From (i) and (ii),
AM = 0.5(0.5AB)
$\Rightarrow \mathrm{AM}=0.25\mathrm{AB}\Rightarrow \mathrm{AM}:\mathrm{AB}=0.25=1:4$