Question

The perpendicular bisector of side
AB
of ∆ABC intersects the side
BC
at point D. Find AB if the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.

Answer 1

Answer:

Let E be the midpoint of side AB, so that DE is the perpendicular bisector of AB.

Then triangle ABD is isosceles; and triangles AED and BED are congruent.

Let F be the point where BC and DE intersect.

Let x be the measure of angle ABC that we are looking for. Then

angle BFE is 90-x [complement of x]

angle BFD is 90+x [supplement of angle BFE]

angle BDF is 74-x [angle sum of triangle BDF, given that angle DBC is 16]

angle ACB is 118 [given]