Mathematics
In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. Prove that:
(i) point A is equidistant from all the three sides of the triangle.
(ii) AM bisects angle LMN.
Locus
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Answer
Steps of construction :
Construct a triangle LMN.
Draw angle bisectors of L and N. Let the angle bisectors meet at A.
Join AM.
(i) Since, A lies on bisector of ∠N
∴ A is equidistant from MN and LN.
Again, as A lies on the bisector of ∠L
∴ A is equidistant from LN and LM.
Hence, proved that A is equidistant from all three sides of the triangle LMN.
(ii) From above part we get,
A is equidistant from MN and LN and also from LN and LM.
We get,
A is equidistant from MN and LM.
∴ A lies on angle bisector of ∠LMN.
Hence, proved that AM bisects ∠LMN.
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