Prove the geometric statements

Discussion in 'Geometry and Trigonometry' started by user156, Sep 29, 2024.

  1. user156

    user156

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    Please provide detailed explanation and guidance. Thank you
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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∘.
    123.jpg
     
    user156, Sep 29, 2024
    #1
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