kiertokulmissa

Kiertokulmissa is a geometric concept linked to circles and cyclic figures. In this context it refers to angles formed by points on a circle, such as inscribed angles and central angles, as well as the properties of figures whose vertices lie on a common circle.

An inscribed angle is formed by two chords that share a common endpoint on the circle; it subtends an arc on the circle. The measure of an inscribed angle is half the measure of its intercepted arc. A central angle is formed by two radii with the vertex at the circle’s center; it subtends the same arc, and its measure equals the measure of the intercepted arc (in the same unit). Angles subtended by the same chord are equal.

A polygon whose vertices all lie on a single circle is called cyclic. In a cyclic quadrilateral, the sum of opposite angles is 180 degrees. More generally, the geometry of cyclic figures imposes relationships between arc measures, chord lengths and angle measures; angles standing on the same chord are equal, and angle sums follow from the circle’s structure.

Applications include solving problems involving arcs, chords and radii, and using angle relations to deduce lengths and positions in cyclic configurations. The chord length relates to the central angle by the formula c = 2R sin(theta/2), where R is the circumradius and theta is the central angle in radians (or the corresponding degree measure).

Overall, kiertokulmissa encompasses key theorems and concepts used to analyze how angles behave in circles and cyclic figures.