Circles Connected With Triangle Assignment Help

Assignment Help: >> Properties of triangles >> Circles Connected With Triangle

Circles Connected With Triangle:

Circumcircle:

The circle passing through vertices of the triangle ABC is called as circum-circle. Its radius R is called as circum radius. In triangle ABC,

280_Circles Connected With Triangle6.png

854_Circles Connected With Triangle.png

In-Circle:

The circle touching 3 sides of the triangle internally is called as inscribed or in-circle of the triangle. Its radius r is called as in-radius of the triangle. In triangle ABC,

47_Circles Connected With Triangle7.png

1118_Circles Connected With Triangle1.png

Remark:       

  • From  2139_Circles Connected With Triangle2.png , we find that r ≤ 4R.1/8 

                        as 1316_Circles Connected With Triangle3.png.

                        Here equality holds for equilateral triangle.

Escribed Circles:

The circle touching BC and the 2 sides AB and AC produced of D ABC externally is called as escribed circle opposite A. Its radius is represented by r1. Likewise r2, and r3 denote the radii of escribed circles opposite to angles B and C respectively. r1, r2, r3 are called as ex-radii of D ABC.  Here

     2388_Circles Connected With Triangle4.png

792_Circles Connected With Triangle5.png

 

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