One base of an isosceles trapezoid is twice the size of the other base. the middle of the larger base

| March 9, 2021 | education

One base of an isosceles trapezoid is twice the size of the other base. the middle of the larger base is spaced from the apex of the obtuse angle at a distance equal to its smaller base. Find the corners of the trapezoid.

By condition, point O from the vertices of an obtuse angle is located at an equal distance OB = OС = BC.

Then the BOС triangle is equilateral with internal angles equal to 60.

Angle BOA = OBC = 60 as criss-crossing angles at the intersection of parallel straight lines ВС and АD secant ОВ. And since, according to the condition, ОА = ОВ, then the triangle AOB is equilateral and therefore the angle BAO = 60.

Then the angle ABC = ABO + OBC = 60 + 60 = 120.

In an isosceles trapezoid, the opposite angles are equal, then the angle ADC = BAD = 60, the angle BCD = ABC = 120.

Answer: The angles of the trapezoid are 60, 120, 60, 120.



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