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Question

In Triangle A B C comma straight angle A D B equals 90 to the power of ring operator. Prove thatA B squared equals A C squared plus B C squared minus 2 B C times C D

hintHint:

Hint :- Applying pythagoras theorem to both triangles ABD and ADC. find the AD2 from both equations  .Equate both the equations to get the required condition .

The correct answer is: Hence proved


    Aim  :- Prove that  A B squared equals A C squared plus B C squared minus 2 B C times C D
    Explanation(proof ) :-Applying pythagoras theorem in Δ ACD ,We get
    A C squared equals A D squared plus C D squared — Eq1
    Applying pythagoras theorem in Δ ABD ,We get
    A B squared equals B D squared plus A D squared not stretchy rightwards double arrow A D squared equals A B squared minus B D squared minus Eq 2
    Substitute Eq1 in Eq2 ,

    A C squared equals A B squared minus B D squared plus C D squared not stretchy rightwards double arrow A C squared equals A B squared plus C D squared minus B D squared

    text  By using  end text a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text  and  end text B C equals B D plus C D text  we get,  end text

                    not stretchy rightwards double arrow A C squared equals A B squared plus left parenthesis B D plus C D right parenthesis left parenthesis C D minus B D right parenthesis

                   not stretchy rightwards double arrow A C squared equals A B squared plus B C left parenthesis 2 C D minus B C right parenthesis

                      A C squared equals A B squared plus 2 B C. C D minus B C squared

                     A C squared plus B C squared minus 2 B C times C D equals A B squared
    therefore space A B squared equals A C squared plus B C squared minus 2 B C times C D
    Hence proved

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