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CBSE Class 9 Answered

Triangle ABCis an isoscles, with AB=AC.If P be any point [n the side BC .prove AP IS LESSER THAN AB.
 
Asked by M.s.srinidhi21 | 17 Jul, 2014, 07:25: PM
answered-by-expert Expert Answer

A B C space i s space a n space i s o s c e l e s space t r i a n g l e A B equals A C P space i s space p o i n t space o n space B C B P plus P C equals B C space C o n s i d e r space t r i a n g l e space A B P comma space A B plus B P greater than A P space left parenthesis s u m space o f space t w o space s i d e s space o f space a space t r i a n g l e space i s space g r e a t e r space t h a n space t h i r d space s i d e right parenthesis space C o n s i d e r space t r i a n g l e space A P C comma space A C plus C P greater than A P space left parenthesis s u m space o f space t w o space s i d e s space o f space a space t r i a n g l e space i s space g r e a t e r space t h a n space t h i r d space s i d e right parenthesis A d d space a b o v e space b o t h space e q u a t i o n s A B plus A C plus B P plus P C greater than 2 A P A B plus A C plus B C greater than 2 A P space C o n s i d e r space t r i a n g l e space A B C comma space A B plus A C greater than B C space left parenthesis s u m space o f space t w o space s i d e s space o f space a space t r i a n g l e space i s space g r e a t e r space t h a n space t h i r d space s i d e right parenthesis space s o space w e space c a n space r e w r i t e space A B plus A C plus B C greater than 2 A P space 2 left parenthesis A B plus A C right parenthesis greater than A B plus A C plus B C greater than 2 A P A B plus A C greater than A P 2 A B greater than A P therefore A P less than 2 A B S o space A P space i s space l e s s space t h a n space 2 space t i m e s space A B

Answered by Dharma Teja | 21 Jul, 2014, 12:59: PM

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