In the figures below, CAD and CBD are congruent (equal in measure), since both are inscribed angles subtended by arc(CD). Any angles that are subtended by the same arc will always be equal.
Any central angle will be double the measure of an inscribed angle subtended by the same arc. Of course, this also means that the inscribed angle is half the measure of the central angle.
The angle inscribed in a semicircle is always a right angle (90°). In other words, any inscribed angle formed by starting from the extremities of a diameter with always measure 90°.
A tangent to a circle is perpendicular (90°) at the point of tangency (T) to the any line that passes through the centre of the circle. In this example, the tangent is perpendicular to the radius at the point of tangency since the radius passes through the centre of the circle.
If a line passing through the centre of the circle is perpendicular to a chord, then that line bisects the chord. Similarly, if a line passing through the centre of the circle bisects a chord, it forms a 90° angle. As well, if a line bisects a chord and is perpendicular to the chord, it passes through the centre of the circle.