In a triangle ABC AB = 5, BC = 3 AC = 7. Point M is located on BC so that the distances from point

In a triangle ABC AB = 5, BC = 3 AC = 7. Point M is located on BC so that the distances from point to straight lines AB and AC are equal. Find MC.

We know that point M is equidistant from AB and AC, which means it lies on the bisector AM of the angle BAC.
We will assume that MC = x, then AB / BM = AC / MC.
We got the proportion, we need to substitute the data and calculate:
5 / (3 – X) = 7 / X;
X = 1.75.
Since x = MC, we found MC = 1.75.
Answer: MS = 1.75.