Alternate segment theorem


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A line that touches a circle at only one point is known as the tangent to the circle. The point that is common to the tangent and the circle is known as the point of contact. The radius or the diameter of the circle drawn at the point of contact is always perpendicular to the tangent.

A chord at the point of contact divides the circle into two segments: The major segment and the minor segment.

Alternate segment theorem: “If a chord is drawn through the point of contact of a tangent to a circle, then the angles that this chord makes with the given tangent are respectively equal to the angles formed in the corresponding alternate segments.” The converse of this theorem also holds good.

This can be proved mathematically.


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