Lesson#1 Circles connected with a triangle Exercise 12.8 Circles connected with a triangle There are three types of circles connected with a triangle. (1) Incircle A circle touching three sides of a triangle internally. Its radius is called in-radius and centre is called incentre. Radius of this circle can be find as, =∆/ 1) ∆ =Area of triangle 2) =(++)/2 (2) Circumcircle: A circle touching three vertices of a triangle externally. Its radius is called circumradius and centre is called circumcentre. Its radius is donoted by . (i) =/(2 sin )=/(2 sin )=/(2 sin) (ii) =/(4 ∆) (3) Escribed Circle: A circle touching one side externally and other two produced sides internally is called Ex-Circle or escribed circle. There can be three circles for one triangle. There radii (plural of radius) are called e-radii, and there centres are called e-centres. (i) Radius of circle opposite to vertex . (ii) Radius of circle opposite to vertex . (iii) Radius of circle opposite to vertex . Application of Trigonometry Chapter No 12 Exercise No 12.8 Mathematics part 1
