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CBSE Class 9 Answered

PROVE THAT ANGLE BISECTOR OF ANY ANGLE OF A TRIANGLE AND PERPENDICULAR BISECTOR OF THE OPPOSITE SIDE IF INTERSECT,THEY WILL INTERSECT ON CIRCUMCIRCLE OF THE TRIANGLE.
Asked by vrishti TOKAS | 22 Feb, 2016, 08:06: PM
answered-by-expert Expert Answer
 
begin mathsize 14px style L e t space t h e space a n g l e space b i s e c t o r space o f space a n g l e space A space i n t e r s e c t space c i r c u m c i r c l e space o f space t r i a n g l e space A B C space a t space D. J o i n space D C space a n d space D B. rightwards double arrow angle B C D equals angle B A D space space space space space space space.... left parenthesis A n g l e s space i n space t h e space s a m e space s e g m e n t right parenthesis rightwards double arrow angle B C D equals angle B A D equals 1 half angle A space space space space.... left parenthesis 1 right parenthesis left parenthesis A D space i s space b i s e c t o r space o f space angle A right parenthesis S i m i l a r l y comma space w e space h a v e angle D B C equals angle D A C equals 1 half angle A space space space space space space... left parenthesis 2 right parenthesis f r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e angle D B C equals angle B C D rightwards double arrow B D equals D C space space space space space space rightwards double arrow D space l i e s space o n space p e r p e n d i c u l a r space b i s e c t o r space o f space B C. H e n c e comma space a n g l e space b i s e c t o r space o f space angle A space a n d space p e r p e n d i c u l a r space b i s e c t o r space o f space B C space i n t e r s e c t space o n space t h e space c i r c u m c i r c l e space o f space triangle A B C. end style
Answered by Rashmi Khot | 23 Feb, 2016, 11:52: AM

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CBSE 9 - Maths
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