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.

Recall the procedure to draw angle bisectors:

  • With B as centre and with a convenient radius draw an arc of a circle to cut AB and AC at X and Y.
  • 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.
  • BS is the angle bisector of B.

  • The angle bisectors pass through a common point (I). This point is called "Incentre".

Note:

The incentre is equidistant from its sides.


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