The angle inscribed in a semicircle is always 90 degrees

Peripheral angle: see 'inscribed angle'

How to construct (draw) a regular pentagon inscribed in a circle. The largest pentagon that will fit in the circle, with each vertex touching the circle.

How to construct (draw) a regular hexagon inscribed in a circle with a compass and straightedge or ruler. This is the largest hexagon that will fit in the circle, with each vertex touching the circle. Ina regular hexagon, the side length is equal to the distance from the center to a vertex, so we use this fact to set the compass to the proper side length, then step around the circle marking off the vertices. A Euclidean construction.

Definition of the incircle of any triangle or regular polygon.

Definition and properties of the inscribed angle of a circle

Definition and properties of the incircle of a triangle