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 | 4th Nov, 2014, 05:23: PM

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 | 4th Nov, 2014, 06:49: PM