OpenGL How to draw curves being part of circle depends of last point location with requirements: fixed radius, last point givig direction

Question

I can not put questions in one line also here they are:

How to draw a curve which is part of the circle(depending on the end point)

Let:

• p1=(x1,y1) be the first point
• have to be line p2=(x2,y2) is the starting point of drawing the curve
• p3=(x3,y3) be the end point (mouse location)

Requirements:

• if P3 is going closer to p2, the larger the potential radius becomes
• p3 describes the drawing direction
• if p3 is pararel to p2 there nothing should be drawn (or drawn line p3>p2)
• if p3 is equal to p1 it should draw a relatively large wheel,

EDIT: I think i found solution how to draw that part of circle, please look at that gifs below:

Answer 1

• Tangent A->B implies a normal-line Q that passes through the (as-yet unfound) circle center D
• Find the midpoint M of chord R (i.e., segment B-C).
• A line S perpendicular to R passing through M also passes through D

So: Construct lines Q and S and find their intersection D. The length of segment B-D is the radius of the circle. With the radius and center D you should be able to calculate the arc B->C.

_{in b4 9000 hours in mspaintpaint.net}