Area Using Semiperimeter

Q.

In acute angled triangle $ABC,r=r_2+r_3-r_1$ and $\angle B>\frac{\pi }{3}$ then exhaustive range of $\frac{a-c}{b}$ is

1. $(\frac{1}{2},1)$

2. $(\frac{1}{4},\frac{1}{2})$

3. $(\frac{1}{4},1)$

4. None of these

Q.

In acute angled triangle $ABC,r+r_1=r_2+r_3$ and $\angle B>\frac{\pi }{3}$ then

1. $b+2c<2a<2b+2c$

2. $b+4c<4a<2b+4c$

3. $b+4c<4a<4b+4c$

4. $b+3c<3a<3b+3c$

Q.

If $A$ is the area and $2s$ the sum of 3 sides of triangle then

1. $A\le \frac{s^2}{3\left(\sqrt{3}\right)}$

2. $A\le \frac{s^2}{2}$

3. $A>\frac{s^2}{\left(\sqrt{3}\right)}$

4. None of these

Q.

In a $△ABC,$ if 2s = a + b + c and (s-b)(s-c)=x $si{n}^2\frac{A}{2},$ then x = [MP PET 1992]

1. bc

2. ca

3. ab

4. abc