Escribed Circle of Triangle - Practice Questions & MCQ

Escribed Circle of Triangle

The circle which touches the side BC and two sides AB and AC produced of triangle ABC is called the escribed circle opposite to the angle A. Its radius is denoted by r₁. Similarly, r₂ and r₃ denote the radii of the escribed circles opposite to the angles B and C respectively. 

Formulae for $r_1, r_2$ and $r_3$
1. $r_1=\frac{\Delta}{s-a}, r_2=\frac{\Delta}{s-b}, r_3=\frac{\Delta}{s-c}$
2. $r_1=s \tan \frac{A}{2}, r_2=s \tan \frac{B}{2}, r_3=s \tan \frac{C}{2}$
3. $r_1=4 R \sin \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}$
$r_2=4 R \cos \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}$
$r_3=4 R \cos \frac{A}{2} \cos \frac{B}{2} \sin \frac{C}{2}$