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CBSE Class 10 Answered

The bisector of interior angle A of triangle ABC meets BC in D, and the bisector of exterior angle A meets BC produced in E. Prove that BD/BE=CD/CE.
Asked by Varsha | 03 Mar, 2019, 08:50: AM
answered-by-expert Expert Answer
Figure shows a triangle ABC. AD is bisector of interior angle A. AE is bisector of exterior angle A.
 
From the property of internal bisector, we have  begin mathsize 12px style fraction numerator B D over denominator C D end fraction equals fraction numerator A B over denominator A C end fraction end style ........................(1)
From the property of external bisector, we have begin mathsize 12px style fraction numerator B E over denominator C E end fraction equals fraction numerator A B over denominator A C end fraction end style .........................(2)
From (1) and (2),  we get begin mathsize 12px style fraction numerator B D over denominator C D end fraction equals fraction numerator B E over denominator C E end fraction space space space space space o r space space space fraction numerator B D over denominator B E end fraction space equals space fraction numerator C D over denominator C E end fraction end style
Answered by Thiyagarajan K | 03 Mar, 2019, 02:58: PM

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