# Circles

### Positions of 2 circles

## Internally TangentIf 2 circles have only one common point which is the point of tangency then they are called internally tangent. Given: (C) and (C') are internally tangent circles with the centers O and O' and radii R and R' So,OO' = R-R' | ## Externally TangentIf 2 circles have one point in common which is the point of tangency then they are called externally tangent. Given:(C) and (C') are tangent externally with the centers O andO' and radii R and R'. So OO' = R+R' | ## Interior CirclesIf 2 circles have no points in common and one is inside the other then they are called interior circles. Given: (C) and (C') are interior circles of centers O and O' and radii R and R' . So OO' < R-R' |

## Internally Tangent

If 2 circles have only one common point which is the point of tangency then they are called internally tangent.

Given: (C) and (C') are internally tangent circles with the centers O and O' and radii R and R'

So,OO' = R-R'

## Externally Tangent

If 2 circles have one point in common which is the point of tangency then they are called externally tangent.

Given:(C) and (C') are tangent externally with the centers O andO' and radii R and R'.

So OO' = R+R'

## For Example

1) What is the position of the 2 circles (C) and (C')?

2) Deduce the measure of OO'.

__Answers:__

1) Since (C) and (C') intersect at 2 points A and B and OO' is the perpendicular bisctor of AB (given) then (C) and (C') are secant

2) Since (C) and (C') are secant then R-R'<OO'<R+R'

## The converse

- If OO' > R + R', then C and AC' are exterior circles
- If OO' < R - R', then C and C' are interior circles with R>R'
- If OO' = R + R', then C and C' are externally tangent circles
- If OO' = R - R', then C and C' are internally tangent circles with R>R'
- If R - R' < OO' < R + R', then C and C' are secant circles with R > R'

## Exterior Circles Given:(C) and (C') are exterior circles of centerss O and O' and radii R and R'. Then OO' > R+R' | ## Secant CirclesIff 2 circles have 2 common points then they are called secant circles. Given:(C) and (C') are secant circles of centers O and O' and radii R and R' . So R-R' < OO' < R+R' |

**Here are some real life examples**