Circles connected with a triangle

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