G Tewani Solutions for Chapter: Solutions and Properties of Triangle, Exercise 4: DPP

In a $∆ABC$ right angled at $A, {\cos }^{-1}\left(\frac{R}{r_2+r_3}\right)$ is

If in a triangle $ABC, r_1=2r_2=3r_3$ and $D$ is the midpoint of $BC,$ then $\cos (\angle ADC)$ is equal to

In the ambiguous case if the remaining angle of a triangle with given $a, b, A$ and $B_1, B_2, C_1, C_2$; then $\frac{\sin C_1}{\sin B_1}+\frac{\sin C_2}{\sin B_2}=?$

Two sides of a triangle are of lengths $\sqrt{6}$ and $4$ and the angle opposite to smaller side $30°$, then how many such triangles are possible?

If circum radius of a triangle $ABC$ is $2$, then the maximum value of $\frac{abc}{a+b+c}$ is?

Let $ABC$ and $A{B}^{\text{'}}C$ be two non-congruent triangles with sides $BC=B^{\text{'}}C=5, AC=6$ and $\angle A$ is fixed. If $A_1$ and $A_2$ are the areas of the two triangles $ABC$ and $A{B}^{\text{'}}C,$ then the value of $\frac{A_1^2+A_2^2-2A_1{A}_2\cos 2A}{{\left(A_1+A_2\right)}^2}$ is

In triangle $ABC$, if $r_1+r_2=3R$ and $r_2+r_3=2R$ then:

The radii $r_1, r_2, r_3$ of the escribed circles of triangle $ABC$ are in harmonic progression. Let area of triangle $ABC$ be $24$ and its perimeter be $24.$ Then which of the following is/(are) correct?