Ex Radius

Q. In a triangle $ABC$ with usual notation, if $r=1,R=3$ and $s=5,$ then which of the following is (are) CORRECT?

1. Area of triangle $ABC$ is $5$ units
2. Product of the sides of triangle$ABC$ is $60$
3. $a^2+b^2+c^2=24$
4. Sum of the ex-radii of triangle $ABC$ is $13$

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. 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

Q. The radii $r_1,r_2,r_3$ of escribed circle of a triangle ABC are in H.P. If its area is $24c{m}^2$ and its perimeter is $24cm$, find the length of its sides.

1. True
2. False

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