The diagonal of an isosceles trapezis with bases 8cm and 5cm is the bisector of the acute

The diagonal of an isosceles trapezis with bases 8cm and 5cm is the bisector of the acute angle of the trapezoid. Find the perimeter of the trapezoid.

Since, by condition, the diagonal AC is the bisector of the angle BAC, then the angle BAC = DAС.
Angle DAС = ВСA as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC.
Then the angle BAC = BCA, and therefore the triangle ABC is isosceles. AB = BC = 5 cm.
Since the trapezoid is isosceles, then AB = СD = 5 cm.
Let’s define the perimeter of the trapezoid. Ravsd = AB + BC + СD + D = 5 + 5 + 5 + 8 = 23 cm.
Answer: The perimeter of the trapezoid is 23 cm.