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Prove that 4 (r1 r2 + r2 r3 + r3 r1) = (...

Prove that `4 (r_1 r_2 + r_2 r_3 + r_3 r_1) = (a+b+c)^2`

Text Solution

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The correct Answer is:
` (a+ b+c)^2`
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In Delta ABC Prove that following 4( r_1r_2+ r_2r_3+r_3r_1) = (a+ b+ c) ^(2)

Prove that r_1 +r_2+r_3-r = 4R

Knowledge Check

  • In Delta ABC , 4 ( r_1r_2 + r_2r_3+ r_3r_1) =

    A
    ` a+ b+c`
    B
    ` (a+ b+ c) ^(2) `
    C
    ` abc`
    D
    ` 0 `

  • In Delta ABC, (r_1+r_2)(r_2+r_3)(r_3+r_1)=

    A
    `4Rs^2`
    B
    `4Rr^2`
    C
    R
    D
    0

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    Prove that (r_1 (r_2 + r_3 ) )/( sqrt( r_1 r_2 + r_2 r_3 + r_3 r_1 ) )= a

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    Prove that r_1^2 + r_2^2 + r_3^2 + r^2 = 16 R^2 - (a^2 + b^2 + c^2) .

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