Secant tangent and tangent tangent angles

How to Determine the Measure of an Angle whose Vertex Is Outside a Circle

secant tangent and tangent tangent angles

Secant-Tangent and Tangent-Tangent Angles. Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. 1). E. F. G ?.

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Note: The term "intercepted arc" refers to an arc "cut off" or "lying between" the sides of the specified angle. Central Angle A central angle is an angle formed by two radii with the vertex at the center of the circle. In a circle, or congruent circles, congruent central angles have congruent arcs. In a circle, or congruent circles, congruent central angles have congruent chords. Inscribed Angle An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.

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A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
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An angle that intersects a circle can have its vertex inside, on, or outside the circle. This article discusses the three types of angles that have their vertex outside a circle: secant-secant angles, secant-tangent angles, and tangent-tangent angles. A tangent is a line that touches a circle at a single point; a secant is a line that intersects a circle at two points. Secant-secant angle: A secant-secant angle, like angle BDF in the above figure on the top left, is an angle whose vertex lies outside a circle and whose sides are two secants of the circle. Secant-tangent angle: A secant-tangent angle, like angle GJK in the above figure on the top right, is an angle whose vertex lies outside a circle and whose sides are a secant and a tangent of the circle. Tangent-tangent angle: A tangent-tangent angle, like angle LMN in the above figure on the bottom, is an angle whose vertex lies outside a circle and whose sides are two tangents of the circle.



11 Secant Tangent and Tangent Tangent Angles

The three theorems for the intercepted arcs to the angle of two tangents, two secants or 1 tangent and 1 secant are summarized by the pictures below. If you look at each theorem, you really only need to remember ONE formula. The angle formed by the intersection of 2 tangents, 2 secants or 1 tangent and 1 secant outside the circle equals half the difference of the intercepted arcs!

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1 COMMENTS

  1. Zacharie A. says:

    Advanced information about circles (Geometry, Circles) Mathplanet

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