Three circles tangent each other
Q01. Diagram
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Q02. Three circles tangent each other and have common tangent
Find radius of smalles circle
- Let radius of one large circle be a
- Let radius of second large circle be b
- Let radius of smallest circle be r3
- Find r3 interm of a and b
Solution
- In right triangle ABD
- AB = a + b
- AD = a - b
- By Pythagorean law, we have BD^2 = AB^2 - AD^2
- Hence BD^2 = (a + b)^2 - (a + b)^2 = 4*a*b
- Hence RT = BD = 2*Sqr(a*b)
- Find radius c of circle C
- Common tangent of circle A and C is RS = 2*Sqr(a*c)
- Common tangent of circle B and C is ST = 2*Sqr(b*c)
- Since RT = RS + ST
- Hence 2*Sqr(a*b) = 2*Sqr(a*c) + 2*Sqr(b*c)
- Simplified we have Sqr(c) = Sqr(a*b)/(Sqr(a) + Sqr(b))
- Hence c = (a*b)/(a + b + 2*Sqr(a*b))
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Q03. Questions
Questions
- 1.
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