How to draw interactive geometrical shapes, that will allow me to drag their corners?

Happy New Year fellows!
I want to create a calculator like this, so the user can enter some values for 2 lines and their angle for a triangle and the program will calculate and report back other info.
It's not that difficult to do this with a
QGraphicsScene
pbject but I also want to drag the edges so that I create my own triangle. After that the spinboxes will be updated with the new data and points and new calculations will be triggered.So my questions are the following:

Can I drag a shape/line/edge/any geometrical entity on a
QGraphicsScene
or anywhere else? 
Can I somehow create a grid that will understand the concept of points and give me the ability to calculate the length of that line, or calculate the area of a triangle?
Is there an API for this or do I have to do the complex mathematics myself?


@Petross404_PetrosS To drag the corner points of a triangle, I would suggest that you find the closest corner point to the mouse point. Move the mouse point to that location and let the user drag that point. Recall that distance can be found by qSqrt(QPointF::dotProduct(p1, p2)).

Hi,
 Yes you can but you have to handle the mouse event yourself.
 Isn't that the role of your shape ?
You can pick the basics on how to do it from this stackoverflow question. Even though it's in python you can pretty easily translate it back to C++.

Thank you both for those hints!