(Dear experts please answer as soon as possible)

ABC is a isoceles triangle in which AB=AC.E is apoint on the side CB produced, such that FE perpendicular to AC.if AD is perpendicular to CB,prove that : AB*FE = AD*EC.
 
 

Asked by pugalatha | 20th Sep, 2015, 11:03: AM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
S i n c e space 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 comma space w e space h a v e comma space A B equals A C A n d space h e n c e comma space angle A B C equals angle A C B T h e space p e r p e n d i c u l a r space f r o m space t h e space v e r t e x space o f space t h e space i s o s c e l e s space t r i a n g l e space b i s e c t s space t h e space o t h e r space s i d e. T h u s comma space A D space b i s e c t s space B C. rightwards double arrow B D equals D C N o w space c o n s i d e r space t h e space t r i a n g l e s comma space A B D space a n d space E C F angle E C F equals angle A C B equals angle A B D angle E F C equals angle A D B equals 90 degree T h u s comma space A A space s i m i l a r i t y comma space w e space h a v e comma space triangle E C F tilde triangle A B D. H e n c e space t h e space c o r r e s p o n d i n g space s i d e s space a r e space p r o p o r t i o n a l. fraction numerator A B over denominator A D end fraction equals fraction numerator E C over denominator E F end fraction rightwards double arrow A B cross times E F equals A D cross times E C

Answered by Vimala Ramamurthy | 20th Sep, 2015, 07:38: PM

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