If two circles have radii 10 cm and 15cm and they touch each other. Find the distance between their centres.

Answer

Distance between their centres is 25 cm or 5 cm .

Explanation

Let the radii of the circles be `r_(1)` and `r_(2)`
`r_(1) = 10cm` and `r_(2) = 15 cm `
By theorem of touching circles, the centres and point of contact are collinear . Here there can be two cases.
Case 1`:`
The circles touch each other externally
Distance between their centres `= r_(1) + r_(2)`
`= 10 + 15`
`= 25 cm `
Case 2 `:`
The circle touch each other internally
Distance between their centres `= r_(2) - r_(1)`
`= 15- 10 `
`= 5 cm `