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CBSE Class 10 Answered

Two circle tough internally.  The sum of their areas is 116pi sq.cm and the distance between their centres is 6cm .Find the radii of the circles.
Asked by lahari lahari | 04 Nov, 2014, 05:23: PM
answered-by-expert Expert Answer
let space the space radii space of space the space circles space be space straight r subscript 1 and space straight r subscript 2. straight r subscript 1 plus straight r subscript 2 equals 6 rightwards double arrow straight r subscript 2 equals 6 minus straight r subscript 1 A subscript 1 plus A subscript 2 equals 116 straight pi rightwards double arrow πr subscript 1 squared plus πr subscript 2 squared equals 116 straight pi rightwards double arrow straight r subscript 1 squared plus left parenthesis 6 minus straight r subscript 1 right parenthesis squared equals 116 space left square bracket Removing space straight pi space from space both space sides right square bracket rightwards double arrow straight r subscript 1 squared plus 36 plus straight r subscript 1 squared minus 12 straight r subscript 1 equals 116 rightwards double arrow 2 straight r subscript 1 squared minus 12 straight r subscript 1 plus 36 minus 116 equals 0 rightwards double arrow 2 straight r subscript 1 squared minus 12 straight r subscript 1 plus 80 equals 0 rightwards double arrow straight r subscript 1 squared minus 6 straight r subscript 1 plus 40 equals 0 rightwards double arrow straight r subscript 1 squared minus 10 straight r subscript 1 minus 4 straight r subscript 1 plus 40 equals 0 rightwards double arrow straight r subscript 1 left parenthesis straight r subscript 1 minus 10 right parenthesis minus 4 left parenthesis straight r subscript 1 minus 10 right parenthesis equals 0 rightwards double arrow left parenthesis straight r subscript 1 minus 10 right parenthesis left parenthesis straight r subscript 1 minus 4 right parenthesis equals 0 therefore straight r subscript 1 equals 10 comma 4 Therefore space straight r subscript 1 equals 10 comma straight r subscript 2 equals 4 Radius space of space the space circles space are space 10 space cm space and space 4 space cm.
Answered by Prasenjit Paul | 04 Nov, 2014, 06:49: PM

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