Q. 55.0( 2 Votes )

In Δ ABC, the bisector of A intersects BC in D. The bisector of ADB intersects AB in F and the bisector of ADC intersects in E. Prove that AF X AB X CE = AE × AC × BF.

Answer :


Given : In Δ ABC, the bisector of A intersects in D. The bisector of ADB intersects in F and the bisector of ADC intersects in E


To prove : AF × AB × CE = AE × AC × BF


Proof : in Δ ABC, the bisector of A intersects at D


1


( in a Δ the bisector of an angle divides the side opposite to the angle in the segments whose lengths are in the ratio of their corresponding sides)


Similarly, In Δ ADB, the bisector of D intersects at F


………………2


And in Δ ADC , the bisector of D intersects at E


…………..eq(3)


Multiplying 1, 2 and 3, we get




And
( )



AF × BD × CE =AE × CD × BF


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Champ Quiz | Thales Theorem49 mins
Quiz | Criterion of Similarity of Triangle45 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
How to Ace Maths in NTSE 2020?36 mins
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :