Two equal circles of radius 10 cm intersect each other and the length of their common chord is 12 cm . Find the distance between the centre of the circle .

Explanation

Let P and Q be two centres of the circle and CD is their common chord . Let the distance between the centre be PQ which intersects CD at O.
`therefore ` O is the mid -point of CD [`because PO bot CD`]
`therefore CO = (1)/(2) CD = (1)/(2) xx 12 cm = 6 cm [ because CD = 12 cm]`
As per question `CP = 10 cm`
Now in the right - angled trinagle ` POC , CP^(2) = OC^(2) + OP^(2)`
or ` (10)^(2) = (6)^(2) +OP^(2) or , OP^(2)= [ because CP = 10 cm , OC = 6cm ]`
or ` 100 =36 + OP^(2) or, OP^(2) = 100 - 36 or OP^(2) = 64 or OP = 8`
` therefore PQ = 2 xx OP [ because OP = OQ]`
` or PQ , = 2 xx 8 cm or , PQ = 16 cm `
Hence the distance between the centres of the circles is 16 cm.