q

Asked by araima2001 | 14th Nov, 2015, 07:11: PM

Expert Answer:

G i v e n space t h a t space angle P A Q equals 70 degree... left parenthesis 1 right parenthesis A l s o space g i v e n space t h a t space T P space a n d space T Q space a r e space tan g e n t s space f r o m space t h e space e x t e r n a l space p o i n t space T. T h u s comma space T P equals T Q rightwards double arrow angle T P Q equals angle T Q P... left parenthesis 2 right parenthesis L e t space u s space c o n s i d e r space t h e space a l t e r n a l e space s e g m e n t space t h e o r e m colon T h e space a n g l e space b e t w e e n space t h e space tan g e n t space a n d space c h o r d space a t space t h e space p o i n t space o f space c o n t a c t space i s space e q u a l space t o space t h e space a n g l e space i n space t h e space a l t e r n a t e space s e g m e n t. space H e r e comma space P space i s space t h e space p o i n t space o f space c o n ta c t space a n d space h e n c e space b y space a l t e r n a t e space s e g m e n t space t h e o r e m comma space w e space h a v e comma angle P A Q equals angle T P Q... left parenthesis 3 right parenthesis F r o m space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma angle T Q P equals angle T P Q rightwards double arrow angle T Q P equals angle T P Q equals 70 degree... left parenthesis 4 right parenthesis C o n s i d e r space t h e space t r i a n g l e space triangle T P Q colon B y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e comma angle T Q P plus angle T P Q plus angle P T Q equals 180 degree rightwards double arrow 70 degree plus 70 degree plus angle P T Q equals 180 degree... open square brackets f r o m space e q u a t i o n space left parenthesis 4 right parenthesis close square brackets rightwards double arrow 140 degree plus angle P T Q equals 180 degree rightwards double arrow angle P T Q equals 180 degree minus 140 degree rightwards double arrow angle P T Q equals 40 degree H e n c e space t h e space c o r r e c t space o p t i o n space i s space left parenthesis D right parenthesis

Answered by Vimala Ramamurthy | 15th Nov, 2015, 10:00: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.