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Show that in a right angled triangle, th...

Show that in a right angled triangle, the hypotenuse is the longest side.

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In a right angle triangle, the hypotenuse is 10 cm more than the shortest side. If third side is 6 cm less than the hypotenuse, find the sides of the right angle triangle.

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Knowledge Check

  • The maximum area of a right angled triangle with hypotenuse h is

    A
    `h^(2)//2 sqrt(2)`
    B
    `h^(2)//2`
    C
    `h^(2)//sqrt(2)`
    D
    `h^(2)//4`

  • In a right angled triangle the hypotenuse is 2sqrt(2) times the perpendicular draen from the opposite vertex. Then the other acute angles of the triangle are

    A
    `(pi)/(3)` and `(pi)/(6)`
    B
    `(pi)/(8)` and `(3pi)/(8)`
    C
    `(pi)/(4)` and `(pi)/(4)`
    D
    `(pi)/(5)` and `(3pi)/(10)`

  • If, in a right angled triangle ABC, the hypotenuse, AB = p, then AB.AC + BC . BA + CA. CB =

    A
    `2 p^(2)`
    B
    `p^(2) // 2`
    C
    `p^(2)`
    D
    none

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    From a circle of radius a, an isosceles right angled triangle with the hypotenuse as the diameter of circle is removed. The distance of the centre of gravity of the remaining portion from the centre of the circle is :

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    Assertion (A) : In Delta ABC if angle B = pi//2 then the diameter of the incircle of the triangle is c+a-b. Reasons ( R ) : In a right angled triangle, hypotenuse is equal to circumradius of circumcircle.

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