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CBSE Class 10 Answered

Prove that the three angle bisectors of the internal angles of a triangle are concurrent.
Asked by rushabhjain.avv | 22 Feb, 2019, 06:53: PM
answered-by-expert Expert Answer
In triangle ABC, CI and BI are angle bisector of angle C and B respectively
we have to prove AI is angle bisector of angle A
construct a perpendicular from I to AC at G, CB at F and AB at E
triangle IGC is congruent to IFC.....AAS test
so IG = IF
triangle IEB is congruent to IFB.....AAS test
so IE = IF
thus IG = IF
in triangle IGA and IEA
IG = IE
hyp IA common 
so they are congruent by Right hypo side test
so
angle GAI = EAI....so AI is bisector of angle A
so all bisectors pass through I...concurrent
Answered by Arun | 23 Feb, 2019, 10:09: AM
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