Question

In the figure, FL=5 and HL=8 what is FM?

Answer 1

We know that
GL=HL/2---------> GL=8/2----> GL=4

in the right triangle FGL
FL=5
GL=4
FG=?
Applying the Pythagoras theorem
FL²=GL²+FG²-----> FG²=FL²-GL²-----> FG²=5²-4²----> FG²=9
FG=3
FG is the radius of the smaller circle
and
FM also is the radius of the smaller circle
so
FM=FG--------> FM=3

the answer is
FM is 3