# tangent of a circle example

16 Perpendicular Tangent Converse. This means that A T ¯ is perpendicular to T P ↔. A circle is a set of all points that are equidistant from a fixed point, called the center, and the segment that joins the center of a circle to any point on the circle is called the radius. This point is called the point of tangency. Proof: Segments tangent to circle from outside point are congruent. 4. 2. Knowing these essential theorems regarding circles and tangent lines, you are going to be able to identify key components of a circle, determine how many points of intersection, external tangents, and internal tangents two circles have, as well as find the value of segments given the radius and the tangent segment. The tangent to a circle is perpendicular to the radius at the point of tangency. We have highlighted the tangent at A. Examples Example 1. Question: Determine the equation of the tangent to the circle: $x^{2}+y^{2}-2y+6x-7=0\;at\;the\;point\;F(-2:5)$ Solution: Write the equation of the circle in the form: $\left(x-a\right)^{2}+\left(y-b\right)^{2}+r^{2}$ Then use the associated properties and theorems to solve for missing segments and angles. Get access to all the courses and over 150 HD videos with your subscription, Monthly, Half-Yearly, and Yearly Plans Available, Not yet ready to subscribe? Example 1 Find the equation of the tangent to the circle x2 + y2 = 25, at the point (4, -3). Yes! Therefore, to find the values of x1 and y1, we must ‘compare’ the given equation with the equation in the point form. Circles: Secants and Tangents This page created by AlgebraLAB explains how to measure and define the angles created by tangent and secant lines in a circle. Therefore, we’ll use the point form of the equation from the previous lesson. Proof of the Two Tangent Theorem. In the figure below, line B C BC B C is tangent to the circle at point A A A. Example 3 Find the point where the line 3x + 4y = 25 touches the circle x2 + y2 = 25. for (var i=0; i