![]() Thus, the alternate segment theorem is proved.įAQs on Alternate Segment Theorem 1. Let P be the point on the circumference of the circle. The angle between the chord and the tangent is equal to the angle made by the chord in the alternate segment. ![]() On the left, we have three valid alternate angles in the alternate segment (and all of them will be equal) for the tangent at P and the chord PQ, whereas, on the right, the angle marked \(\gamma\) is not the alternate angle for the tangent at P, since it is on the same side of the chord PQ (same segment) as the tangent at P. ![]() Alternate Segment Theorem ExamplesĬonsider the figures given below. This angle will be the same regardless of the position of R (as long as R stays in the segment opposite the tangent). Let \(\angle PRQ = \angle \beta \), the alternate angles in the alternate segment for the angle between the tangent at P and the chord PQ. Suppose that PQ subtends an angle \(\beta\) at a point R anywhere on the circumference of the circle, as shown: ![]() Suppose that a tangent is drawn to a circle such that the point of contact is P, and through P, a chord PQ is drawn which is inclined to the tangent at an angle \(\alpha\). What Do You Mean by the Alternate Segment Theorem ? Alternate Segment Theoremįor any circle, the angle between a tangent and a chord through the point of contact of the tangent is equal to the angle made by the chord in the alternate segment. ![]()
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