There are four points A,B,C,D on the plane, such that any three points are not collinear. Prove that in triangles ABC, ABD, ACD, BCD there is at least one triangle which has an interior angle not greater than 45 degree.

There are four points A,B,C,D on the plane, such that any three points

1.	There are four points A,B,C,D on the plane, such that any three points are not collinear. Prove that in triangles ABC, ABD, ACD, BCD there is at least one triangle which has an interior angle not greater than 45 degree.
Answer» There are four points A,B,C,D on the plane, such that any three points are not collinear. Prove that in triangles ABC, ABD, ACD, BCD there is at least one triangle which has an interior angle not greater than 45 degree.

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There are four points A,B,C,D on the plane, such that any three points are not collinear. Prove that in triangles ABC, ABD, ACD, BCD there is at least one triangle which has an interior angle not greater than 45 degree.

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