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In the isosceles triangle △ABC, AB = AC.
Its circumscribed circle has a centre at point M, which lies inside the triangle. Show that all the following statements are equivalent with each other:
Statement (1): The triangle △ABC is equilateral.
Statement (2): The radius MB is a bisector of angle B.
Statement (3): The angle BMC is 120∘.
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In the isosceles triangle △ABC, AB = AC.
Its circumscribed circle has a centre at point M, which lies inside the triangle. Show that all the following statements are equivalent with each other:
Statement (1): The triangle △ABC is equilateral.
Statement (2): The radius MB is a bisector of angle B.
Statement (3): The angle BMC is 120∘.
