Embibe Experts Solutions for Chapter: Properties of Triangle, Exercise 1: JEE Main - 10th January 2019 Shift 2

Let $\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)},$ where $A, B, C$ are angles of a triangle $ABC.$ If the lengths of the sides opposite these angles are $a, b, c$ respectively, then

In $\mathrm{\Delta ABC},$ the lengths of sides $AC$ and $AB$ are $12 \mathrm{cm}$ and $5 \mathrm{cm},$ respectively. If the area of $∆\mathrm{ABC}$ is $30{ \mathrm{cm}}^2$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $\mathrm{\Delta ABC}$, then the value of $2R+r \left(\text{in cm}\right)$ is equal to ______ .

If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

The angles $A, B \& C$ of a $∆ABC$ are in $A.P.$ and $a:b=1:\sqrt{3}.$ If $c=4 cm,$ then the area (in $sq. cm$) of this triangle is:

With the usual notation in $∆ABC$, if $\angle A+\angle B=120°, a=\sqrt{3}+1$ units and $b=\sqrt{3}-1$ units, then the ratio $\angle A:\angle B$ is

Let $a,b$ and $c$ be the length of sides of a triangle $ABC$ such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$. If $r$ and $R$ are the radius of incircle and radius of circumcircle of the triangle $ABC$, respectively, then the value of $\frac{R}{r}$ is equal to

Let $C$ be the centre of the circle $x^2+y^2-x+2y=\frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$, makes an angle of $\frac{\pi }{4}$ with the line $CP$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $PQR$ (in ${\mathrm{unit}}^2$) is

For a triangle $ABC$, the value of $\cos 2A+\cos 2B+\cos 2C$ is least. If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?