JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Properties of Triangle

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi }{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

Let a be the area of the triangle …

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi }{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

Then the inradius of the triangle …

Let PQRS be a quadrilateral in a plane, where $QR=1$, $\angle PQR=\angle QRS=70^{\circ }$, $\angle PQS=15^{\circ }$ and $\angle PRS=40^{\circ }$. If $\angle RPS={\theta }^{\circ }$, $PQ=\alpha$ and $PS=\beta$, then the interval(s) that contain(s) the value of …

In a triangle ABC, let $AB=\sqrt{23},BC=3$ and $CA=4$. Then the value of $\frac{\cot A+\cot C}{\cot B}$ is ____.

Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?

Let x, y and z be positive real numbers. Suppose x, y and z are lengths of the sides of a triangle opposite to its angles X, Y and Z, respectively. If

then which of the following statements is/are TRUE?