In the adjoining figure,quadrilateral ABCD is circumscribed. If the radius of the incircle with centre O is 10 cm and ADperpendicularDC, find the value of x.

Asked by pankaj.sharma12378 | 6th Jan, 2016, 10:04: PM

Expert Answer:

T h e space d a t a space g i v e n space i n space t h e space q u e s t i o n space s e e m s space i n s u f f i c i e n t space f o r space f i n d i n g space x. I n s t e a d space o f space A B comma space i f space w e space t a k e space P B space a s space 27 space c m space a s space s h o w n space i n space t h e space f i g u r e space a b o v e comma space w e space c a n space p r o c e e d space a s space f o l l o w s space t o space f i n d space x comma space t h e space l e n g t h space o f space C D. I n space q u a d r i l a t e r a l space O S D R comma space angle D equals 90 degree angle O R D equals 90 degree angle O D S equals 90 degree D S equals D R space left parenthesis l e n g t h s space o f space tan g e n t s space f r o m space t h e space s a m e space p o i n t space D right parenthesis O S D R space h a s space a l l space a n g l e s space a s space r i g h t space a n g l e s space a n d space t w o space a d j a c e n t space s i d e s space a r e space e q u a l. H e n c e comma space i t space i s space a space s q u a r e. H e n c e comma space R D equals O S equals 10 space c m B P equals B Q equals 27 space c m space left parenthesis tan g e n t s space f r o m space s a m e space p o i n t space B right parenthesis Q C equals B C minus B Q rightwards double arrow Q C equals 38 minus 27 equals 11 space c m C R equals C Q equals 10 space c m space left parenthesis l e n g t h s space o f space tan g e n t s space f r o m space s a m e space p o i n t space C right parenthesis H e n c e comma space x equals C D equals R D plus C R equals 10 plus 11 equals 21 space c m

Answered by satyajit samal | 8th Jan, 2016, 03:07: PM

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