4.2 Draw a circle with radius 100

Scratch solution

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View solution

This is just one of many possible solutions:

when green flag clicked
clear
go to x: (0) y: (0)
point in direction (90 v)
set [pi v] to [3.1415]
set [radius v] to [100]
move (radius) steps
point in direction (0 v)
pen down
repeat (360)
  move ((((radius) * (2)) * (pi)) / (360)) steps
  turn ccw (1) degrees
end
pen up

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Extra Challenge

Extra challenge #1: Write a program that works for any radius. That means that it takes a radius as the input then draws a circle with the given radius, and then displays the circumference as the output.

Extra challenge #2: Write a program that takes a circumference as the input then draws a circle with the given circumference and then displays the radius as the output.

Extra challenge #3: [This requires advanced maths, but is a good challenge for a student who is familiar with Pythagoras' theorem] Draw a Circle Using Pythagoras’ Theorem.

A red circle drawn using the Pythagoras' Theorem method.

The diagram above shows a circle (radius 100) drawn using the Pythagoras’ Theorem method. (Note: The red triangle inside the circle is only to show the calculation and does not need to be drawn).

You can use Pythagoras’ Theorem (in any right-angle triangle, the square of the side opposite the right angle is equal to the sum of the squares of the other two sides so here $x^{2}+y^{2}=radius^{2}$ ) to draw a circle. We can do this by rearranging the formula to solve for $y$ like this:

$y^{2} = radius ^{2} - x^{2} \\ y = sqrt{(radius^{2} - x^{2})}$

We then calculate $y$ using a range of values for $x$ (i.e. from 0 to $\pm radius$ ). Your programming language will probably only give you the positive square root, so you will also need to plot the negative of $y$ .