# In triangle ABC, angle B is 20 °, angle C is 40 °. The bisector of AD equals 2. Find the difference between the sides BC and AB.

January 17, 2021 | education

| Determine the value of the angle BAC. Angle BAC = (180 – 40 – 20) = 120.

Since the BP is bisector, the angle ВAD = СAD = 120.

From vertex A we construct a segment AE so that the angle CAE = 40, then the triangle ACE is isosceles, and the angle AEC = 180 – 40 – 40 = 100.

AED angle adjacent to AEC angle, AED angle = 180 – 100 = 80.

The angle DAE = CAD – СAE = 60 – 40 = 200, then the angle ADE = (180 – 20 – 80) = 80, and then the triangle ADE is isosceles, AE = AD = 2 cm, and then CE = AE = 2 cm.

In triangle ABE, the angle BAE = (60 + 20) = 80, then the angle AEB = (180 – 80 – 20) = 80, which means that the triangle ABE is isosceles, AB = AE.

Then BC – AB = BC – AE = CE = 2 cm.

Answer: The difference between the sides BC and AB is 2 m.

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