A tangent line to a circle intersects the circle at exactly one point on its circumference. The radius drawn from the center of the circle to the point of tangency is always perpendicular to the tangent line.
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In this lesson we’ll look at inscribed angles of circles and how they’re related to arcs, called intercepted arcs. A chord is a straight line segment that has endpoints on the circumference of the circle, and an inscribed angle is formed by two chords. These chords share the vertex of an angle. The arc that touches the endpoints of the chords is called the intercepted arc.
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A chord of a circle is a line segment that has both of its endpoints on the circumference of a circle. The intersecting chord theorem says that the product of intersecting chord segments will always be equal, so we can use this theorem to solve problems involving chords of circles.
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In this lesson we’ll look at angles whose sides intersect a circle in certain ways and how the measures of such angles are related to the measures of certain arcs of that circle.
As we work through this lesson, remember that a chord of a circle is a line segment that has both of its endpoints on the circle. Besides that, we’ll use the term secant for a line segment that has one endpoint outside the circle and intersects the circle at two points. Finally, we’ll use the term tangent for a line that intersects the circle at just one point.
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The area of a circle is given by A=πr^2, where π is the constant approximately equal to 3.14, and r is the radius of the circle. The radius r is the distance from the center of the circle to the edge of the circle. The diameter of the circle is double the radius; it’s the distance from one side of the circle to the other, through the center of the circle.
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Given the equation of a circle, we can put the equation in standard form, find the center and radius of the circle from the standard form, and then use the center and radius to graph the circle. Alternately, given the graph of the circle, we can identify the center and radius from the graph and then plug those values into the standard equation of the circle in order to get its equation.
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There’s a special relationship between two secants that intersect outside of a circle. The length outside the circle, multiplied by the length of the whole secant is equal to the outside length of the other secant multiplied by the whole length of the other secant.
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