7/23/2023 0 Comments Chord geometry real life![]() A chord is a portion of the secant with its endpoint on the secant line. Is Secant of a Circle and the Chord of a Circle the Same? ![]() In other words, if the chord is extended on both sides it becomes the secant. A secant line includes the chord and is always extended outside the circle. The secant-tangent rule states that when a secant line and a tangent line are drawn both from a common exterior point, the product of the secant and its external segment is equal to the square of the tangent segment.įAQs on Secant of a Circle What is the Secant of a Circle?Ī line that intersects the circle exactly at two distinct points is the secant of the circle.The intersecting secants theorem states that if we draw two secant lines from an exterior point of a circle, the product of one secant and its external segment is equal to the product of the other secant and its external segment.A secant of a circle is a line that connects two distinct points on a curve.Here is a list of a few points that should be remembered while studying about the secant of a circle: \(\alpha = \dfrac]\)Ĭheck out here for a few interesting topics related to secant of a circle: The angle subtended by the tangent and the secant at the exterior is half the difference of the major arc and the minor arc intercepted by them.The product of the secant and its exterior segment is equal to the square of the tangent segment. ![]() Secant segments are AB (interior) and BC(exterior). The secant AC and the tangent CD are drawn from the same exterior point.Observe the figure given above to see that: Tangent Secant TheoremĪccording to the tangent secant theorem, if a secant and a tangent are drawn to a circle from a common exterior point, then the product of the length of the whole secant segment and its external secant segment is equal to the square of the length of the tangent segment. The tangent is perpendicular to the radius at the point of the tangency. ![]() The main difference between them is that a secant cuts the circle at two points, whereas, a tangent cuts the circle at one point. Tangents and secants are the lines that cut the circle and extend in both directions infinitely. The angle formed by the two secants which intersect outside the circle is half the difference of the intercepted arcs.The angle formed by the two secants that intersect inside the circle is half the sum of the intercepted arcs.There are two theorems based on this property of secants. In the second circle, the secants intersect outside the circle and the major arc PT and minor arc QS are intercepted by the secants. In the first circle, the secants intersect inside the circle and major arc AD and minor arc BD are intercepted by the secants. In the circles shown below, we find that the intersecting secants inside and outside create angles x and y at the points of intersection, respectively. Two secants can intersect inside or outside a circle. Thus, according to the theorem, we have AB × AD = AC × AE Secants and Angle Measures AD is the external secant segment of the whole secant segment AB, and AE is the external secant segment of AC. In the figure shown above, we find that AB and AC are the two secant segments intersecting at point A. This is also known as the secant theorem or the secant power theorem. The intersecting secants theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment.
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