Related to this idea of an inscribed angle is that of an inscribed triangle. A triangle is said to be inscribed in a circle if all of the vertices of the triangle are points on the circle.
The figure that follows shows a special case of the rule mentioned here (that an inscribed angle is equal to half of the arc it intercepts, in degrees). In this case, the right angle (90°) lies opposite a semicircle, which is an arc that measures 180°.
The important rule to remember is: If one of the sides of an inscribed triangle is a diameter of the circle, then the triangle must be a right triangle. Conversely, any right triangle inscribed in a circle must have the diameter of the circle as one of its sides (thereby splitting the circle in half).
The inscribed triangle ABC must be a right triangle, because AC is a diameter of the circle.
