Show that all circles share identical shapes. Examine the relationship between inscribed angles, radii, and chords. Explain the association between central, inscribed, and circumscribed angles; note that inscribed angles situated on a diameter form a right angle; describe how a circle's radius is perpendicular to the tangent line at the point of intersection with the circle.

Construct the inscribed and circumscribed circles of a triangle and substantiate properties of angle measures for a four-sided figure placed in a circle. Develop a tangent line from an external point to a given circle.

Using similarity, establish that the arc length confined by an angle relates proportionally to the radius, and outline the radian measure of the angle as the constant of this proportionality. Generate the formula for the sector's area.