Circles inscribed in a segment

A circle can be inscribed in a segment of a circle (called a circular segment), meaning the circle fits perfectly inside the segment and touches its boundary at exactly three points: the two endpoints of the chord and a point on the arc. The largest such circle is called the 'inscribed circle' of the segment.

Important properties

• The inscribed circle is tangent to the chord and the arc of the segment.

• The center of the inscribed circle lies on the angle bisector of the angle formed at the endpoints of the chord (when viewed from the center of the original circle).

• The radius of the inscribed circle depends on the radius of the original circle and the length of the chord.