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Let ABC be a triangle in which the line ...

Let ABC be a triangle in which the line joining the circumecentre and incentre is parallel to base BC of the triangle. Then answer the following questions :
Then range of `angle A` is

A

`[(pi)/(6),(pi)/(3)]`

B

`[(pi)/(3),(pi)/(2))`

C

`[(pi)/(3),(2pi)/(3)]={(pi)/(3)}`

D

`[0,(pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
B

`because` The line joining O and I is parallel to BC
`therefore OI = DE` and OD = IE
OD = R cos A, IE = r
`therefore cos A = (r )/(R ) le (1)/(2)`
`rArr 0 lt cos A le (1)/(2)rArr (pi)/(3)le A lt (pi)/(2)`
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Knowledge Check

  • For a triangle ABC, which of the following is true?

    A
    cosA/a=cosB/b=cosC/c
    B
    `cosA/a+cosB/b+cosC/c=(a^2+b^2+c^2)/(2abc)`
    C
    `sinA/a+sinB/b+sinC/c=3/(2R`
    D
    `(sin2A)/a^2=(sin2B)/b^2=(sin2C)/c^2`

  • In triangle ABC which of the following is not true :

    A
    `vec(AB)+vec(BC)+vec(CA)=vec(0)`
    B
    `vec(AB)+vec(BC)-vec(AC)=vec(0)`
    C
    `vec(AB)+vec(BC)-vec(AC)=vec0`
    D
    `vec(AB)-vec(CB)+vec(CA)=vec(0)`

  • In any triangle ABC, which of the following is false?

    A
    a=b cos C - c cos B
    B
    `sin A + sin B gt sin C`
    C
    `b^(2) = c^(2) + a^(2)-2ca cosB`
    D
    The formula `a^(2) = b^(2) - 2bc cosA` can be deduced using the formula of the form `a= b cos C + c cosB`

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