A luminous point P is inside a circle. A ray emanates from P and after two reflections by the circle,returns to P. If θ be the angle of incidence, a= the distance of P from the centre of the circle and b=the distance of the centre from the point where the ray in its course crosses its diameter through P. prove that tan θ=((a−b)/(a+b))


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Question Number 57664 by necx1 last updated on 09/Apr/19

$A l u m i n o u s p o i n t P i s i n s i d e a c i r c l e .$ $A r a y e m a n a t e s f r o m P a n d a f t e r t w o$ $r e f l e c t i o n s b y t h e c i r c l e, r e t u r n s t o P .$ $I f θ b e t h e a n g l e o f i n c i d e n c e, a = t h e$ $d i s t a n c e o f P f r o m t h e c e n t r e o f t h e$ $c i r c l e a n d b = t h e d i s t a n c e o f t h e c e n t r e$ $f r o m t h e p o i n t w h e r e t h e r a y i n i t s$ $c o u r s e c r o s s e s i t s d i a m e t e r t h r o u g h P .$ $p r o v e t h a t \tan θ = \frac{a - b}{a + b}$
Commented by mr W last updated on 10/Apr/19

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