Ex Radius

Q.

In a triangle, if $r_1=2r_2=3r_3,then\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ is equal to

1. 

2. 
   

3. 

4. 

Q.

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_1}{r_2}-\frac{r_2}{r_3}$

1. 1

2. 0

3. 2r

4. None

Q. The radii $r_1,r_2,r_3$ of the escribed circles of the triangle $ABC$ are in H.P. If the area of the triangle is $24{\text{cm}}^2$ and its perimeter is $24\text{cm}$, then the length of its largest side is

1. $10$
2. $9$
3. $8$
4. $7$

Q. Relation between Exradius , semiperimeter and circumradius can be given by
($r_1$ is the radius of the circle opposite the angle A)

1. $r_1=\frac{2\Delta }{s-a},r_1=4Rcos\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
2. $r_1=\frac{\Delta }{s-a},r_1=4Rsin\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$
3. $r_1=\frac{2\Delta }{(s-a)(s-b)},r_1=4Rcos\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
4. $r_1=\frac{\Delta (s-a)}{(s-b)(s-c)},r_1=4Rcos\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$

Q. If $r_1,r_2,r_3$ represent the exradii and r represents the inradius then, $\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}-\frac{1}{r}$ = 0

1. True
2. False

Q. In $△ABC,R,r,r_1,r_2,r_3$ denote the circumradius, inradius, the exradii opposite to the vertices $A,B,C$ respectively. Given that $r_1:r_2:r_3=1:2:3$.
The sides of the triangle are in the ratio

1. $1:2:3$
2. $3:5:7$
3. $1:5:9$
4. $5:8:9$

Q. If $r_1,r_2,r_3,s,△,a,b,c$ are the standard notations then which of the following is correct?

1. $r_1=\frac{△}{s-a}$
2. $r_2=\frac{△}{s-b}$
3. $r_3=\frac{△}{s-c}$
4. All of the above