In triangle ABC, point M is the midpoint of side AB and angle A is equal to angle B. Prove that angle ACB is equal to 2 angle AFM.
Let’s take a look at the figure to solve it.
By condition, the angles CAB and CBA are equal to each other, therefore, the triangle ABC is isosceles, in two angles.
Since, according to the condition, point M divides AB into equal parts, AM = BM, the straight line drawn from point C to point M is the height, median and bisector of triangle ABC, according to the properties of an isosceles triangle.
Angle АСВ = АСМ + ВСМ.
The bisector CM divides the angle into two equal angles, AFM = BCM, therefore, ASB = 2 * AFM, which was required to prove.
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