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In a non right angled triangle DeltaPQR,...

In a non right angled triangle `DeltaPQR`, let `p,q,r` denote the lengths of the sides opposite to the angle P,Q,R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. if `p=sqrt(3),q=1` and the radius of the circumcircle of the `DeltaPQR` equals to 1, then which of the followign options is/are correct?

A

Length of RS `=sqrt7/2`

B

Area of `DeltaSOE=sqrt3/12`

C

Length of OE `=1/6`

D

Radius of incircle of `DeltaPQR =sqrt3/2 (2-sqrt3)`

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