# 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. 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. Zacharie A. says: