The point on a tangent that is on the circle. Example: Point x A secant B Point of Tangency C Tangent D Radius 2. A line that intersects a circle at wo points
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Michael A.
40.) A line in the plane of a circle that intersects the circle at two points is the a. tangent b. secant c. radius d. diameter
Elizabeth W.
The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. See the figure. If the equation of the circle is $x^{2}+y^{2}=r^{2}$ and the equation of the tangent line is $y=m x+b,$ show that: (a) $r^{2}\left(1+m^{2}\right)=b^{2}$ [Hint: The quadratic equation $x^{2}+(m x+b)^{2}=r^{2}$ has exactly one solution.] (b) The point of tangency is $\left(\frac{-r^{2} m}{b}, \frac{r^{2}}{b}\right)$ (c) The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.
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