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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 `OE = (1)/(6)`

B

Length of `RS = (sqrt(7))/(2)`

C

Length of `DeltaSOE = (sqrt(3))/(12)`

D

Radius of incircle of `DeltaPQR = (sqrt(3))/(2)(2-sqrt(3))`

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The correct Answer is:
ABD
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