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In the given figure ABC is a right angle...

In the given figure ABC is a right angled triangle with `angleB=90^(@) ` . D is the mid -point of BC . Show that `AC^(2) = AD^(2) +3CD^(2)` .

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In a triangle ABC,B=90^(@) and D is the mid-oint of BC then prove that AC^(2)=AD^(2)+3CD^(2)

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Knowledge Check

  • ABC is a right triangle with angleB=90^(@) and AC - AB = 1. If BC=sqrt(n) then AB is

    A
    `(n+1)/(2)`
    B
    `(n-1)/(2)`
    C
    `n/2`
    D
    `(n-3)/(2)`

  • If ABC is a right angled triangle at B and M, Nare the mid-points of AB and BC, then 4(AN^2+CM^2) is equal to :

    A
    `4AC^2`
    B
    `6AC^2`
    C
    `5AC^2`
    D
    `5/4AC^2`

    • Similar Questions

    Explore conceptually related problems

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    In Fig.3,ABC is a right triangle,right angled at C and D is the mid-point of BC.Prove that AB^(2)=4AD^(2)-3AC^(2)

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    In a right ABC right-angled at C, if D is the mid-point of BC, prove that BC^(2)=4(AD^(2)-AC^(2))

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