10 thoughts on “Triangles – Examples 4

  1. Yes, when I first encountered this one, I spent over 3 minutes trying for a formal solution before seeing that it needs to be greater than 35 😦 And the other method I noticed only on revisiting the problem later – at the second try it struck me quite quickly 😛 Very tricky one to visualise.

    regards
    J

  2. Here is how I solved this question:

    A( ) — Denotes angle
    S( ) — Denotes side

    Construction : Join BD
    Obseration : A( CBD ) = A( CBD )

    So,
    A( CBD ) = [ 180 – (y+20) ] / 2 = ( 160 – y ) / 2
    A( CDB ) = [ 180 – (y+20) ] / 2 = ( 160 – y ) / 2

    A( ABD ) = 140 – A( CBD) = (120 + y) / 2
    A( ADB ) = 110 – A( CDB ) = ( 60 + y ) / 2

    A( BAD ) = x + 20

    Assumption : y S(DC) > S(AD)

    Also , in triangle ABD we know that A( ABD ) > A( ADB )

    (2) Therefore , in triangle ABD ==> S(AD) > S(AB)

    But , we know that S(DC) = S(AB) . Hence , (1) and (2) contradicts each other that means our assumption is wrong .

    Now checking values of x and y for the following cases:

    y x Compare

    20 50 y < x
    30 40 y x

    So, the correct option is (3) .

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