In a non-right-angled triangle | Maths | JEE ADVANCED 2019

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JEE ADVANCE 2019

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Question

In a non-right-angled triangle $\triangle P Q R$, 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 $P Q$ at $S$, the perpendicular from $P$ meets the side $Q R$ at $E$, and $R S$ and $P E$ intersect at $O$. If $p=\sqrt{3}, q=1$, and the radius of the circumcircle of the $\triangle P Q R$ equals 1 , then which of the following options is/are correct?

Select ALL correct options:

A

Area of $\triangle \mathrm{SOE}=\frac{\sqrt{3}}{12}$

B

Radius of incircle of $\triangle \mathrm{PQR}=\frac{\sqrt{3}}{2}(2-\sqrt{3})$

C

Length of $\mathrm{RS}=\frac{\sqrt{7}}{2}$

D

Length of $\mathrm{OE}=\frac{1}{6}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

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