In <mi mathvariant="normal">&#x0394;<!-- Δ --> A B C , B E and C F a

Feinsn

Feinsn

Answered question

2022-06-13

In Δ A B C, B E and C F are the angular bisectors of B and C meeting at I. Prove that A F / F I = A C / C I
I have tried this question for hours but i am unable to hit the nut
I tried to using: (1)Similarity (2)Angle bisector theorem (3)Relation of lengths of angle bisector :- B E 2 + A E . E C = A B . B C C F 2 + A F . F B = A C . B C
I tried the question with these many approaches but i unable to prove the above relation.please tell if any of these approach will help or please tell any other method to solve the question.

Answer & Explanation

Jaida Sanders

Jaida Sanders

Beginner2022-06-14Added 18 answers

Hint: The ratio of the area of A F I and the area of A C I is given by F I / C I, and also by A F / A C.
Layla Velazquez

Layla Velazquez

Beginner2022-06-15Added 11 answers

Since A I is a bisector of Δ A F C, we obtain:
A F A C = F I C I
or
A F F I = A C C I
and we are done!

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