Q. 95.0( 1 Vote )

In ΔABC, the bisector of A intersects in D and the bisector of ADC intersects in E. Prove that AB × AD × EC = AC × BD × AE.

Answer :

Given, In ABC, the bisector of A intersects in D and the bisector of ADC intersects in E as shown in figure.


To prove: AB × AD × EC = AC × BD × AE


Proof: In ∆ABC, the bisector of A intersects BC in D.


...... (i)


In ∆ADC, the bisector of ADC intersects AC in E.


...... (i)


By multiplying eq (i) and (ii)




AB × AD × EC = AC × BD × AE


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