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In triangle $ABC,$ $M$ is the midpoint of $\overline{AB}.$ Let $D$ be the point on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC,$ and let the perpendicular bisector of $\overline{AB}$ intersect $\overline{AD}$ at $E.$ If $AB = 44$ and $ME = 12,$ then find the distance from $E$ to line $AC$.

May 16, 2020

#2
+21953
+1

AD is the bisector of angle(A).

Every point on the bisector of an angle is equally distant from the two sides of the angle.

The distance from a point to a side of the angle is measured by the perpendicular distance to the side.

ME is perpendicular to AB and the length of ME is 12; this is the distance from the point to the side of the angle.

Therefore, the distance from E to AC is also 12.

May 16, 2020

#1
0

This is easy!  The distance from E to AC is 22.

May 16, 2020
#2
+21953
+1

AD is the bisector of angle(A).

Every point on the bisector of an angle is equally distant from the two sides of the angle.

The distance from a point to a side of the angle is measured by the perpendicular distance to the side.

ME is perpendicular to AB and the length of ME is 12; this is the distance from the point to the side of the angle.

Therefore, the distance from E to AC is also 12.

geno3141 May 16, 2020