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Question

straight angle A of an isosceles triangle ABC is acute in which  AB = AC and BDperpendicularAC . Prove that
B C squared equals 2 cross times A C cross times C D text .  end text

The correct answer is: Hence proved


    Solution :-
    Aim  :- prove B C squared equals 2 cross times A C cross times C D
    Hint :- Using pythagoras theorem, find the length of  side AB and BC .
    Substitute the RHS of  B C squared equals C D squared plus B D squared in terms of AC and CD Explanation(proof 

     Using pythagoras theorem,in triangle BDC
    B C squared equals C D squared plus B D squared minus Eq 1
    Using pythagoras theorem,in triangle BDA
    A B squared equals B D squared plus A D squared not stretchy rightwards double arrow B D squared equals A B squared minus A D squared minus Eq 2
    Substitute Eq2 in Eq1
    B C squared equals A B squared minus A D squared plus C D squared
    Substitute AD = AC - CD (from diagram)
    B C squared equals A B squared minus left parenthesis A C minus C D right parenthesis squared plus C D squared not stretchy rightwards double arrow B C squared
    equals A B squared minus A C squared minus C D squared plus 2 cross times A C cross times C D plus C D squared

    text  As  end text A B equals A C left parenthesis text  given  end text right parenthesis text  we get,  end text B C squared equals A C squared minus A C squared minus C D squared plus 2 cross times A C cross times C D plus C D squared
    not stretchy rightwards double arrow B C squared equals 2 cross times A C cross times C D
    Hence proved

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