I am trying to solve a geometry problem. as first step I am trying to construct it on Geogebra:
To complete the construction I need to draw a circle which passes through the point $O$ and is tangent to the line $AB$ and also tangent inside the circle which passes through $AB$ (the bigger circle).
So the center of this circle is a point which has the same distance to the line and to the point $O$ and to the circle but I don't know how I can find this point.
Consider the point of tangent of the circle to be constructed and link it to $O$. It is a radius of the big circle so it is perpendicular to the tangent line. Thus this line is also the diameter of the circle to be constructed. Knowing this, we know that the radius of this circle is half that of the large circle.
Now construct a circle with half the radius and with center $O$, along with a parallel line that is that same distance away (in pink). The intersections would be the centers of the circles to be constructed.
