there-is-two-small-and-one-grater-circles-that-two-are-tangent-to-one-and-all-three-circles-are-inscribed-in-an-ellipse-with-a-b-2-2-and-tangent-to-it-at-two-points-such-that-center-of-circ

Question Number 49736 by behi83417@gmail.com last updated on 10/Dec/18

there is two small and one grater circles

that [two] are tangent to [one] and all three

circles are inscribed in an ellipse with :

[\frac{a}{b} = 2 \sqrt{2}] and tangent to it at two points such that center

of circles are on major axe of ellipse .

find : \frac{radi of great circle}{radi of small circle} .

Commented by ajfour last updated on 10/Dec/18

Answered by ajfour last updated on 10/Dec/18

l e t b = 1, a = 2 \sqrt{2}

e q . o f e l l i p s e : \frac{x^{2}}{8} + y^{2} = 1

e q . o f l a r g e r c i r c l e : x^{2} + y^{2} = 1

e q . o f s m a l l e r c i r c l e :

{(x - r - 1)}^{2} + y^{2} = r^{2}

f o r t a n g e n c y w i t h e l l i p s e,

{(x - r - 1)}^{2} + (1 - \frac{x^{2}}{8}) = r^{2} h a s

o n l y o n e r o o t . \Rightarrow

\frac{7}{8} x^{2} - 2 (r + 1) x + 2 (r + 1) = 0

o r 7 x^{2} - 16 (r + 1) x + 16 (r + 1) = 0

\Rightarrow 16 \times 16 {(r + 1)}^{2} = 7 \times 4 \times 16 (r + 1)

\Rightarrow 4 r + 4 = 7 \Rightarrow r = \frac{3}{4}

\frac{R a d i u s o f g r e a t e r c i r c l e}{R a d i u s o f s m a l l e r c i r c l e} = \frac{1}{3 / 4} = \frac{4}{3} .

Commented by behi83417@gmail.com last updated on 10/Dec/18

t h a n k s a l o t s i r A j f o u r .

c a n y o u d r a w a p r o p e r p i c t u r e f o r t h i s

q u e s t i o n p l e a s e ? i {c a n}^{'} t i n s t a l l lekh diagram .

i n 4 t h l i n e f r o m e n d : x i s m i s s i n g .

Commented by ajfour last updated on 10/Dec/18

y e s S i r, b u t w h a t s t h e t r o u b l e i n

i n s t a l l i n g L e k h D i a g r a m ?

Commented by behi83417@gmail.com last updated on 10/Dec/18

t h a n k y o u v e r y m u c h s i r .

i t i s n o t a v a i l a b l e i n g o o g l e p l a y f o r m e .