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,
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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,
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Remark:
- From , we find that r ≤ 4R.1/8
as .
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
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