Maharashtra State BoardSSC (English Medium) 7th Standard
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The Property of the Angle Bisectors of a Triangle

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  • Incentre

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The Property of the Angle Bisectors of a Triangle:

  • Draw any ΔPQR.
  • Use a compass to draw the bisectors of all three of its angles. (Extend the bisectors, if necessary, so that they intersect one another.)
  • These three bisectors pass through the same point. That is, they are concurrent.
    Name the point of concurrence ‘I’. Note that the point of concurrence of the angle bisectors of a triangle is in the interior of the triangle.
  • Draw perpendiculars IA, IB, and IC respectively from I on to the sides of the triangle PQ, QR, and PR. Measure the lengths of these perpendiculars. Note that IA = IB = IC.

Point to Remember:

The angle bisectors of a triangle are concurrent. Their point of concurrence is called the incentre, and is shown by the letter ‘I’.

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