Circle

[cunning berry]

I don't know how to apply unit vector for this question? is there another way to do this?

[cunning berry]

Here is my working

And here is where I got confuse

[runic hare]

You could apply unit vectors for this, but ... why?

I'd find the coordinates of the orange point using the fact that ||it partitions the blue segment in a ratio of 1:4||

Further hint: ||(5,2) is the midpoint of this segment||

As a check, $C_3$ passes through $(2.4, -1.2)$.

[mystic nimbus]

Civil Service Pigeon

[cunning berry]

You mean something like this?

[runic hare]

,rotate

[runic hare]

Those are the coordinates of the orange point

[cunning berry]

so like that the centre for circle c3?

[runic hare]

not necessarily

[cunning berry]

It stated that all three circle lie on a straight line, so is it possible that entire straight be the diameter for C3?

[runic hare]

,rotate

[runic hare]

yup that's the motivation behind everything I said

we're thinking in terms of that diameter

[cunning berry]

Now that i got the radius how do i find the centre😭

[runic hare]

you have three points: the two centres and their tangency point

focus on each circle individually

knowing that you have two points for each circle: the centre and the tangency point

[runic hare]

you can uncover this if you need to

[cunning berry]

So far am I correct?

[runic hare]

Idk but this is way too much

The midpoint of that long diameter is the center of C3

[cunning berry]

Yup got it now thx

,rotate

[cunning berry]

Extra proof ig

.closed

[runic hare]

.close