Question

prove in any triangle abc if one angle is 120 degree the triangle formed by feet of angle bisectors is right angled​

Answer 1

Answer:

Therefore the triangle formed by the feet’s of angle bisectors of triangle whose one angle measure is 120  

∘

 is Right Triangle.

Step-by-step explanation:

Let Triangle ABC, ∠A=120  

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Let AD, BE, CF are angle bisectors of A, B, C respectively.

In ΔABD, AC is exterior angles bisector (as ∠DAC=∠CAX=60  

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).

BE is internal angle bisector meet at E . E is ex-center of ΔABD

So DE is exterior angle bisector of ΔABD

Then, ∠ADE=∠EDC,∠ADC=2∠ADE.

Similarly we can prove that for the ΔABC, F is ex-center as AB is exterior angle bisector and CF is interior angle bisector.

Hence DF is exterior angle bisector.

∠ADF=∠FDB,∠BDA=2∠ADF

BC is straight angle.

∠BDA+∠ADC=180  

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2∠ADF+2∠ADE=180  

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∠ADF+∠ADE=90  

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Hence DEF is right triangle.

Therefore the triangle formed by the feet’s of angle bisectors of triangle whose one angle measure is 120  

∘

 is Right Triangle.

solution