Tool for drawing and colouring shapes easily

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I want a tool to easily make geometry diagrams. For example, say I wish to overlay two circles, and then fill their overlap with the color red, whilst coloring other areas with other colors? Let's say I want to make a triangle with curved sides and a flat bottom side; that could be done in no time with the right tool. I could insert a square and then delete circles from its upper two quadrants. To be more clear, here are the list of features I'd like:

  1. A gallery of shapes that can be sized and colored as one wishes.
  2. The ability to fill any area enclosed by lines with a color.
  3. The ability to draw lines between highlighted points on shapes, like the centers of their sides, their corners, points between the quadrants of the circumference of a circle (allowing the drawing of diameters), etc.
  4. The ability to insert text into the diagrams.
  5. Is free to use.

To give examples of close contenders: Draw.io has all features except number two. Microsoft paint and sketchpad has all features except number three. Does an app that has all features exist?