Three circles of radii a, b, c (a＜b＜c) touch each

Question

Three circles of radii a, b, c (a＜b＜c) touch each other externally. If they have x axis as their common yangent, then: 1/√ a = 1/√ b + 1/√ c	1/√ b = 1/√ a + 1/√ c	a, b, c are in AP	√ a, √ b, √ c are in APplz explain too

Aditya Gupta · Accepted Answer

dear student there is a theorem called Descartes' circle theorem for 4 kissing circles (you can google it and look up the wikipedia article for more info and refer the SPECIAL CASES section).using that, we observe that (k1+k2+k3)^2= 2(k1^2+k2^2+k3^2) where k1, k2 and k3 are a, b, c respsimplifying k1^2+k2^2+k3^2= 2(k1k2+k2k3+k3k1)k1^2 – 2k1(k2+k3) + (k2 – k3)^2= 0or k1= k2+k3 ± 2sqrt(k2k3)k1= [sqrt(k2) ± sqrt(k3)]^2or sqrt(k1)= sqrt(k2) ± sqrt(k3)1/sqrt(a)= 1/sqrt(b) ± 1/sqrt(c)since a＜b＜c, -ve sign is not possiblehence 1/√ a = 1/√ b + 1/√ cKINDLY APPROVE :))

Analytical Geometry> Three circles of radii a, b, c (a＜b＜c) to...

Three circles of radii a, b, c (a＜b＜c) touch each other externally. If they have x axis as their common yangent, then:

1/√ a = 1/√ b + 1/√ c

1/√ b = 1/√ a + 1/√ c

a, b, c are in AP

√ a, √ b, √ c are in AP
plz explain too

AD , 5 Years ago

Aditya Gupta

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Analytical Geometry> Three circles of radii a, b, c (a＜b＜c) to...

Three circles of radii a, b, c (a＜b＜c) touch each other externally. If they have x axis as their common yangent, then: 1/√ a = 1/√ b + 1/√ c 1/√ b = 1/√ a + 1/√ c a, b, c are in AP √ a, √ b, √ c are in APplz explain too

AD , 5 Years ago

Aditya Gupta

LIVE ONLINE CLASSES

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Three circles of radii a, b, c (a＜b＜c) touch each other externally. If they have x axis as their common yangent, then:

1/√ a = 1/√ b + 1/√ c

1/√ b = 1/√ a + 1/√ c

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√ a, √ b, √ c are in AP
plz explain too