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](https://www.expertsmind.com/CMSImages/280_Circles%20Connected%20With%20Triangle6.png)
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![854_Circles Connected With Triangle.png](https://www.expertsmind.com/../CMSImages/854_Circles Connected With Triangle.png)
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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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![47_Circles Connected With Triangle7.png](https://www.expertsmind.com/CMSImages/47_Circles%20Connected%20With%20Triangle7.png) |
![1118_Circles Connected With Triangle1.png](https://www.expertsmind.com/../CMSImages/1118_Circles Connected With Triangle1.png)
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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![2388_Circles Connected With Triangle4.png](https://www.expertsmind.com/../CMSImages/2388_Circles Connected With Triangle4.png)
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![792_Circles Connected With Triangle5.png](https://www.expertsmind.com/../CMSImages/792_Circles Connected With Triangle5.png)
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