Question

Let M be the midpoint of side \overline{AB} of \triangle ABC. Angle bisector \overline{AD} of \angle CAB and the perpendicular bisector of side \overline{AB} meet at X. If AB = 40 and MX = 9, then how far is X from line {AC}?

Answer 1

Answer: 9

Step-by-step explanation:

According to the statement we have

AD is bisecting the angle <CAB

and Perpendicular bisector of overline AB i.e. CM is meeting at X.

Now, AB=40 and MX= 9.

We can already relate that the two triangles

AMX and AEX are congruent that means,

the ratio of sides are equal i.e. AM/EX= AM/MX

or EX= MX

Now, MX= 9 so EX=9 which is actually the distance of X from line AC