11.2.2 Angle Relationships in Circles (continued)
The measure of an angle formed by a tangent and a secant to a circle is determined in this example. The measures of the arcs intercepted by the angle are given. The measure of the angle is equal to twice the difference between the arcs intercepted by the tangent and secant. Substituting the given values into the formula gives x = (1/2)(120 ° − 50 ° ) = 35 ° . The measure of an angle formed by two tangents to a circle is determined in this example. The measures of the arcs intercepted by the angle are given. The measure of the angle is equal to twice the difference between the arcs intercepted by the tangents. Substituting the given values into the formula gives y = (1/2)(220 ° − 140 ° ) = 40 ° .
Example 4 Cycling Application
The measure of an angle formed by two secants to a circle is determined in this application example. The measures of the arcs intercepted by the angle are given. The measure of the angle is equal to twice the difference between the arcs intercepted by the secants. Substituting the given values into the formula gives m ∠ ACE = (1/2)(50 ° − 10 ° ) = 20 ° .
262
Made with FlippingBook - PDF hosting