. In the given figure, two equal circles, with centres O and O', touch each other at X. OO' produced me the circle with centre O' at A. AC is tangent to the circle with centreO, at the point C. O'D is perpendicular to AC. Find the value of `(DO')/(CO)`.

Explanation

`/_ADO’ = 90^0 `( tangent to the circle is perpendicular to the radius through the point of contact )

In` /_\ADO’ and `/_\ACO`

`/_ADO’ = /_ACO` ( both are 90^0)

`/_DAO’=/_CAO` (common point )

`:. /_AO’D=/_AOC`

BY AAA criterion of congruence ` /_\ADO’ ` and` /_\ACO` are congruent

`:. (AO’)/(AO) = (DO’)/(CO)`

And` AO= AO’ + O’X + OX `

...