In the ABC triangle, the angle is C = 60 degrees. Point D is marked on the AC side so that the angle BDC

| January 15, 2021 | education

In the ABC triangle, the angle is C = 60 degrees. Point D is marked on the AC side so that the angle BDC = 60 degrees, and the angle ABD = 30 degrees. Prove that BP = BC. Prove that the perimeter of triangle ABC is less than five lengths BC.

Since two internal angles in the ВСD triangle are equal to 600, the ВСD triangle is equilateral.
Let BC = СD = ВD = X cm.
In the AED triangle, the ADВ angle is adjacent to the ВDС angle, then the ADВ angle = (180 – 60) = 1200.
Then the angle ВAD = (180 – 120 – 30) = 300, and therefore the triangle AВD is isosceles, AD = ВD = X cm.
The perimeter of the triangle ABC = AB + BC + AC = AB + X + 2 * X = AB + 3 * X.
AB cannot be more than 2 * X, then Ravs is less than 5 * X and less than 5 * BC, which was required to be proved.



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