Made for some funny exams afterwards...

The first was that my father purchased a PC in the early 1990s to help out with his self-employed publishing business, and like most PCs of the time, it came preloaded with QBasic and the source code for a couple of games like GORILLA.BAS that an introverted kid with a lot of free time could mess around with.

The second was attending a high school with a reasonably well funded computer lab and an unusually open minded computer teacher. If you demonstrated that you were dependable, he'd basically let you do whatever you want. While my school was mostly a Mac shop, I was a bit of a Microsoft shill in high school so by graduation I'd figured out how to stand up and run a Windows NT file & web server for our school newspaper. Another guy was a Linux nut and had been allowed to do something similar with RedHat for the school's drafting lab.

Inclination met opportunity, one thing led to another, and I went on to work with technology for the next 25 years of my life.

What worries me now is that so much technology is so locked down. It must be a very rare school today that allows the kind of freedom we had. There is no IDE preinstalled on a phone, and even merely installing an "unapproved" app is under fire.

If for no other reason, for the sake of the kids the industry, the tools, the operating systems need to be more open. They need to be tinkerable. That's how the most motivated kids tend to learn. Our best and brightest are not being made because we've closed things down to maximize some hedge fund's ROI somewhere. The financialization of America was a grave error.

I'm going to make two assumptions based on your screenshot:

1. The large circles A and B are touching each other

2. You know the radius (a,b,c) of each circle and want the third one (circle C) to touch both of the first two.

What I'd do is place the center of both circles A and B on the same horizontal line and choose a frame of reference such that the center of circle A is the origin, and the center of circle B is placed at coordinates (a+b, 0)

Now we are looking for the coordinates (x, y) of the center of circle C, placed above the x-axis. Which by the way is one of two solutions, as there is a symmetrical circle C' placed below the x-axis, with the coordinates (x, -y)

We know that if we traced a straight line from the center of C, it would intersect the x-axis at a 90° angle. So drawing that line creates two triangles which each have a right angle in this spot:

- one triangle on the left, where the hypothenuse goes from the center of A (0,0) to the center of C (x,y). Its length is the sum of the radii of A and C.

- one triangle on the right, where the hypothenuse goes from the center of B (a+b,0) to the center of C (x,y). Its length is the sum of the radii of B and C.

Both of these triangles share a vertical segment of length (y).

The left triangle's bottom segment has a length of (x) and the right triangle's bottom segment has a length of: (a+b) - x

We know from Pythagore that the square of the length of the hypothenuse is equal to the sum of the squares of the two sides of each triangle, so we know that:

    (a+c)^2 = x^2 + y^2

    (b+c)^2 = ((a+b) - x)^2 + y^2

    y^2 = (a+c)^2 - x^2 = (b+c)^2 - ((a+b) - x)^2

    (a+c)^2 - x^2 = (b+c)^2 - ((a+b) - x)^2

    a^2 + c^2 + 2ac - x^2 = b^2 + c^2 + 2bc - ((a+b)^2 + x^2 - 2ax - 2bx)

    a^2 + 2ac = b^2 + 2bc - (a^2 + b^2 + 2ab - 2ax - 2bx)


    a^2 + 2ac = 2bc - a^2 - 2ab + 2ax + 2bx

    2 a^2 + 2ac - 2bc + 2ab = 2ax + 2bx

        a^2 + ac + ab - bc
    x = ------------------
               a+b

I did notice that in your screenshot A and B are of the same size, so if you knew this from the start it becomes way simpler.

x = a (of course the center of your new circle is at the vertical of the point where both circles touch, which is obvious due to the symmetry of the problem)

and

y = squareroot(c^2 + 2ac)

40 years later, and I've successfully managed to never use a Microsoft product.

People sometimes underestimate how important search engines are to build applications without official documentation.

Supporting FOSS is more than a convenience for some, as most remember locked ecosystems were not fun at any age. I remember GW-Basic and VB3.0 made building programs easy for kids, but it had other issues besides the license cost. Prior to Visual studio, making standalone binaries was simply too difficult for most until the Internet.

Now the average AAA game is around 40GiB on Steam, and g++/clang is the standard tool-suites. Fun times, =3

https://www.folklore.org/MacBasic.html

I think they became less interesting because they became more homogenous, more standardized, more commercialized

It's like the internet. It was more interesting when everything was spread out and you felt like you had to explore it. Now it's all the same content collected on the same 5 sites, and it feels like there's nothing actually interesting out there anymore