Maths-
General
Easy

Question

In △ABC, ∠B=90 and  is the mid point of BC. Prove that A C squared minus A D squared equals 3 B D squared
 

The correct answer is: Hence proved


    Hint :- use pythagoras theorem in triangle ABD and ABC

    Hint :- use pythagoras theorem in triangle ABD and ABC
    We get AC squared and AD squared subtract them and substitute BC = 2BD
    In the equation to get the result.
    Explanation(proof ) :-
    Applying pythagoras theorem in triangle ABC,we get
    A C squared equals A B squared plus B C squared  —- Eq1
    Applying pythagoras theorem in triangle ABD ,we get
    AD squared equals AB squared plus BD squared Eq2
    As AD is median , D is mid point then BC = 2BD
    Subtract Eq1 - Eq2
    We get, AC squared minus AD squared equals AB squared plus BC squared minus open parentheses AB squared plus BD squared close parentheses
    AC squared minus AD squared equals BC squared minus BD squared text  substitute  end text BC equals 2 BD
    AC squared minus AD squared equals 4 BD squared minus BD squared
    AC squared minus AD squared equals 3 BD squared
    Hence proved

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