Given that two circles touch y-axis and line y=(1/sqrt(3)) x.
if the centre of both circles lie on the line y = sqrt(3) x
what is the distance between the centre of both circles?

any hint? :)

Question

Given that two circles touch y-axis and line y=(1/sqrt(3)) x. 
if the centre of both circles lie on the line y = sqrt(3) x
what is the distance between the centre of both circles?

any hint? :)

chihiroasleaf · Answer

sorry..., I mistype the question...,
the centre of both circles lie on the line y = sqrt (3)

sirm3d · Answer

hmm, i got 4 for an answer.

sirm3d · Answer

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hartnn · Answer

two circles with radius 1 and 3, so distance between centres = sum of radius =4,( as both the circles touch y-axis)
could u find radius of each circle ?

hartnn · Answer

the line has slope of 1/sqrt 3, so the angle that the line makes with x-axis =30 degrees

hartnn · Answer

so u get 2 , 30-60-90 triangles, from where u can get radius of both circles

sirm3d · Answer

the coordinate of the first center is (-b,sqrt(3)), then use the distance of a point from a line (y=sqrt(3)x) which is also b.

sirm3d · Answer

oops, i think i made some mistake in my algebra.

sirm3d · Answer

my algbra is correct. the answer is still 4. what did you get, @hartnn ?

hartnn · Answer

even i get 4.

hartnn · Answer

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