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