Question

Which of the following relations hold true ?

• A. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
• B. $r=\frac{\Delta }{s},r=Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
• C. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{3}sin\frac{B}{3}sin\frac{C}{3}$
• D. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{3}sin\frac{B}{2}sin\frac{C}{2}$

Answer 1

The correct option is A $r=\frac{\Delta }{s},r=2Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$

Relation between in radius, Area of triangle and semiperimeter can be given by $r=\frac{\Delta }{s}$ and relation between inradius and circumradius can be given by $r=2Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$