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Properties of Triangle question

2019 · Shift 1 · Q25

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PYQ Library
JEE Advanced
Mathematics
Properties of Triangle
2019 · Shift 1 · Q25

Properties of Triangle question

2019 · Shift 1 · Q25

JEE AdvancedMathematicsProperties of TriangleMultiple correct+4 / −1

In a non-right-angled triangle

\Delta

PQR, let p, q, r denote the lengths of the sides opposite to the angles At 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

\Delta

PQR equals 1, then which of the following options is/are correct?

A
Length of OE = ${1 \over 6}$
B
Length of RS = ${{\sqrt 7 } \over 2}$
C
Area of $\Delta$ SOE = ${{\sqrt 3 } \over {12}}$
D
Radius of incircle of $\Delta$ PQR = ${{\sqrt 3 } \over {2}}$ ( ${2 - \sqrt 3 }$ )

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