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| Concurrency of the angle bisectors of a triangle |
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| Draw a triangle ABC. Draw its angle bisectors. The angle bisectors pass through a point. |
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| Recall the procedure to draw angle bisectors: |
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With B as centre and with a convenient radius draw an arc of a circle to cut AB and AC at X and Y. |
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With X and Y as centres and radius equal to more than half of XY draw arcs of circles to intersect at S. Join BS. |
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BS is the angle bisector of B. |
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The angle bisectors pass through a common point (I). This point is called "Incentre". |
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| The incentre is equidistant from its sides. |
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