geometry problem

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  • #21769
    swastik pramanik
    Participant

    A triangle ABC is inscribed in a circle of radius 1, with <BAC = 60 degree. Altitudes AD and BE of triangle ABC intersect at H. Find the smallest possible value of the length of the segment AH.

    #21776
    Tarit Goswami
    Moderator

    First observe that length of the segment \( AH = 2R\cos{\angle{BAC}} \) , where \( R\) is the circumradius.

    So, $$AH = 2\cdot \cos{60^o} = 1$$

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