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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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