Triangle

Q. If $5,5r,5r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to :

1. $\frac{7}{4}$
2. $\frac{3}{2}$
3. $\frac{3}{4}$
4. $\frac{5}{4}$

Q. If $x,y,z$ are non-negative integers such that $2(x^3+y^3+z^3)=3(x+y+z{)}^2$, then maximum value of $x+y+z$ is

Q. In triangle $ABC$, If $(1-\frac{r_1}{r_2})(1-\frac{r_1}{r_3})=2$, then the triangle is:

1. Isosceles
2. Equilateral
3. Right angled
4. Obtuse angled

Q. In a triangle $ABC,$ the value of$\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}=$

1. $\frac{a+b+c}{\Delta }$
2. $\frac{a^2+b^2+c^2}{{\Delta }^2}$
3. $\frac{a^2+b^2+c^2}{\Delta }$
4. $\frac{a+b+c}{{\Delta }^2}$

Q. In the diagram below, $A$ and $B(20,0)$ lie on the $x$-axis and $C(0,30)$ lies on the $y$-axis such that $\angle ACB={90}^{\circ }.$ A rectangle $DEFG$ is inscribed in $△ABC.$ Given that the area of $△CGF$ is $351$ sq. units. Then $\frac{1}{9}\left(\text{area of rectangle}DEFG\right)$ is
(correct answer + 3, wrong answer 0)

Q. If $x,y,z$ are non-negative integers such that $2(x^3+y^3+z^3)=3(x+y+z{)}^2$, then maximum value of $x+y+z$ is

Q. With usual notation in a $△ABC,$ if $(\frac{1}{r_1}+\frac{1}{r_2})(\frac{1}{r_2}+\frac{1}{r_3})(\frac{1}{r_3}+\frac{1}{r_1})=\frac{K{R}^3}{a^2{b}^2{c}^2},$ then $K$ has the value equal to

Q. If $5,5r,5r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to :

1. $\frac{3}{2}$
2. $\frac{3}{4}$
3. $\frac{5}{4}$
4. $\frac{7}{4}$

Q. Draw triangle $ABC$ on your notebook. Draw a line segment equal to the sum of any two sides of the triangle. Name it as $\overline{DE}$

Q. If $5,5r,5r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to :

1. $\frac{3}{2}$
2. $\frac{3}{4}$
3. $\frac{5}{4}$
4. $\frac{7}{4}$

Q. With usual notation in a $△ABC,$ if $(\frac{1}{r_1}+\frac{1}{r_2})(\frac{1}{r_2}+\frac{1}{r_3})(\frac{1}{r_3}+\frac{1}{r_1})=\frac{K{R}^3}{a^2{b}^2{c}^2},$ then $K$ has the value equal to