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| Theorem 1 |
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| "The point of concurrency of the angle bisectors of the angles of triangle, is called the incentre". It is abbreviated as 'I'. |
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| To determine the incentre of a triangle, it is just sufficient to find the point of intersection of its two angles. The third angle bisector is bound to pass through it by virtue of the below theorem. |
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| The angle bisectors of a triangle pass through the same point. |
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| In the above theorem we have proved ID = IE = IF. That is, if a circle with centre I and radius = ID (or IE or IF) is drawn, the circle will pass through the points D, E and F. This circle is called the incircle of a triangle, the centre of incircle is called incentre and the radius of incircle is called inradius. |
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