11.1.1 Lines That Intersect Circles (continued)
The length of the leg of a right triangle that is tangent to a circle is determined in this application example. The length of one leg of the triangle is given. To solve this example, recognize that the line of sight from the mountain top to the horizon is a tangent line with the point of tangency as the endpoint to be measured to. The radius of Earth forms a right angle with the point on the horizon. The hypotenuse that forms a right triangle with the radius and line of sight is a line from the center of Earth to the point of view on top of the mountain. The length of the hypotenuse is the radius of Earth plus the height of the mountain, or 4003.84 mi. Use the Pythagorean Theorem to find the length of the unknown leg, the distance to the horizon. The distance is approximately 175 mi.
Example 4 Using Properties of Tangents
Two line segments drawn from one point external to a circle to points of tangency with the circle are congruent.
The length of a line tangent to a circle is determined in this example. The length of two lines tangent to a circle and drawn from the same external point are given as algebraic expressions. Since they extend from one point external to a circle and are both tangent to the circle, BC ≅ DC and BC = DC . Set up an equation that equates the given expressions for the lengths of the two line segments and solve for x . To find BC , substitute x = 3 into the expression for the length. The solution yields BC = 6.
171
Made with FlippingBook Annual report maker