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Find the value of (a^2+b^2+c^2)/R^2 in a...

Find the value of `(a^2+b^2+c^2)/R^2` in any right-angled triangle.

Text Solution

Verified by Experts

The correct Answer is:
8
Let `angle A = (pi)/(2) rArr a^(2) = b^(2) + c^(2) and 2R = a`
`rArr (a^(2) + b^(2) c^(2))/(R^(2)) = (2a^(2))/(R^(2)) = (2a^(2) xx4)/(a^(2)) = 8`
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Knowledge Check

  • In a right angled triangle a^2+b^2+c^2 is :

    A
    `R^2`
    B
    `4R^2`
    C
    `8R^2`
    D
    none of these

  • Statement I In any right angled triangle (a^(2)+b^(2)+c^(2))/(R^(2)) is always equal to 8. Statement II a ^(2)=b^(2) +c^(2)

    A
    Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I
    B
    Both Statement I and Statement II are correct and Statement II is not the correct explanation of Statement I
    C
    Statement I is correct but Statement II is incorrect
    D
    Statement I is correct but Statement I is incorrect

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