Project Euler Forum

Not sure about

That is, both the radius and the distance to the origin are scaled by the same factor, and the centre of rotation is the origin.

Say C1 has center (x1, y1), radius r1 and C0 has center (x0, y0), radius r0. Is it true that r1=f*r0 and x1^2+y1^2=f^2*(x0^2+y0^2) such that 0<f<1?
Thanks.

@pickdig: Yes, that is true.

I'm confused what the question means by the total area. Surely the area depends on the distance from C_0 to the origin. I notice that the question specifically says to find the area "in the diagram" but I assume I'm not expected to stick a ruler against my monitor.
EDIT: Somehow in reading the question a dozen or so times, I missed the words "unit circle"

I think I've come up with a solution for this problem but I feel that all that I have wrong is precision. I'm at a loss as to how I can get the correct solution to 10 digits. I got .0555... and .0823... for the area of the two circular triangles touching C0. I'm confident they are right because I made a geogebra drawing that shows these areas to several decimal places.

I've calculated the distances between circle centers using a couple different methods (one by the centers themselves and one by the radii of the circles) and the difference is very small, but enough to throw the last 3 of the ten required digits of the collective area off.

I don't know if I'm asking for things I shouldn't ask here, but what could possibly be the problem? If anyone has any advice I'd sure appreciate it.

I had it right. I didn't put a zero in front of the decimal point. Pretty stupid on my part, but the directions didn't say to do it. I think other problems that called for a decimal value between zero and one specifically asked for the zero. Oh well. I guess those 2 values might be a help to others.

thomjackson wrote: Sat Nov 09, 2024 1:43 pm I didn't put a zero in front of the decimal point.

That is really really unfortunate. I don't know if it's necessary since that is definitely well known standard notation, but maybe there should be some section on the site for input formatting where things like this can be mentioned. Could include an explanation of significant digits for people who haven't seen it either.