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In any triangle ABC, if 2Delta a-b^(2)c=...

In any triangle ABC, if `2Delta a-b^(2)c=c^(3)`, (where `Delta` is the area of triangle), then which of the following is possible ?

A

B is obtuse

B

A is obtuse

C

C is obtuse

D

B is right angle

Text Solution

Verified by Experts

The correct Answer is:
B
`2Delta a-b^(2)c=c^(3)`
`rArr 2Delta a^(2)b=abc(b^(2)+c^(2))`
`rArr ((a^(2)b)abc)/(2R)=abc(b^(2)+c^(2))`
`rArr (a^(2)b)/(2R)=b^(2)+c^(2)`
`rArr a^(2)sin B=b^(2)+c^(2)`
If sin B = 1, then `a^(2)=b^(2)+c^(2)`, which is not possible
`thereofre sin B ne 1`
`therefore cos A = (b^(2)+c^(2)-a^(2))/(2bc)`
`=(a^(2)sinB-a^(2))/(2bc)`
`lt 0`
`therefore` A is obtuse
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