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three circles of radius 2cm touch one another externally.these circle are circumscribed by a cirlce of radius R=4.3 cm.find the value  of R and area of d shaded region
 
 
 
Asked by Chandana kiran | 23 Feb, 2015, 12:48: AM
answered-by-expert Expert Answer
 
Let space straight O space is space the space center space of space the space larger space circle. Let space straight R space be space the space radius space of space the space larger space circle. increment ABC space is space an space equilateral space triangle. angle BCA equals 60 degree angle OCE equals 30 degree In space increment OEC comma CE equals 2 space cm space left parenthesis radius space of space the space circle right parenthesis cos space 30 degree equals CE over OC rightwards double arrow fraction numerator square root of 3 over denominator 2 end fraction equals 2 over OC rightwards double arrow OC equals fraction numerator 4 over denominator square root of 3 end fraction space cm Radius space of space the space larger space circle comma space straight R equals 2 space plus space OC equals open parentheses 2 plus fraction numerator 4 over denominator square root of 3 end fraction close parentheses space cm Area space of space the space shaded space region space equals πR squared minus 3 πr squared equals straight pi open square brackets open parentheses 2 plus fraction numerator 4 over denominator square root of 3 end fraction close parentheses squared minus 3 cross times 2 squared close square brackets equals straight pi open square brackets fraction numerator 16 square root of 3 minus 8 over denominator 3 end fraction close square brackets space cm squared
Answered by Prasenjit Paul | 23 Feb, 2015, 12:15: PM

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