Let M be the midpoint of side AB of triangle ABC. Angle bisector of AD of angle CAB and the perpendicular bisector of side AB meet at X. If AB=40 and MX=9,

Here is what I believe you describe :

AD bisects angle CAB, CM is the perpendicular bisector of AB

XM = 9, AB = 40

And triangle AMX ≈ triangle AEX  .....so..... AX/MX  = AX/EX .......so......MX = EX     ....and  EX is the distance from X to AC = 9

Another very nice answer Chris :)

You are becoming an expert at using GeoGebra    -:))

these geometry questions that Mellie is presenting are really fun. :)