3. Let P be a point on a circle C. Then a line P is defined to be tangent to C at P if it intersects C exactly at P, that is, PC={P}. Assume that every point P of a circle C has a unique tangent line through it (we will prove this later) and that the circle C lies entirely within one of the closed half-planes of every such tangent. Use this to prove that any disk (whether open or closed) is convex. 3. Let P be a point on a circle C. Then a line P is defined to be tangent to C at P if it intersects C exactly at P, that is, PC={P}. Assume that every point P of a circle C has a unique tangent line through it (we will prove this later) and that the circle C lies entirely within one of the closed half-planes of every such tangent. Use this to prove that any disk (whether open or closed) is convex