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In DeltaABC, bc=2b^(2)cos A+2c^(2)cos A-...

In `DeltaABC, bc=2b^(2)cos A+2c^(2)cos A-4bc cos^(2)A`, then `Delta ABC` is

A

isosceles but not necessarily equilateral

B

equilateral

C

right angled but not necessarily isosceles

D

right angled isosceles

Text Solution

Verified by Experts

The correct Answer is:
A
`bc=2b^(2)cos A+2c^(2)cos A-4bc cos^(2)A`
`rArr bc=2 cos A(b^(2)+c^(2)-2bc cos A)`
`rArr bc=(2 cos A)a^(2)`
`rArr (bc)/(2a^(2))=cos A=(b^(2)+c^(2)-a^(2))/(2bc)`
`rArr b^(2)c^(2)=a^(2)(b^(2)+c^(2)-a^(2))`
`rArr (a^(2)-b^(2))(a^(2)-c^(2))=0`
Thus, triangle is isosceles.
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