Concept explainers
To calculate: The measure of third arc from the help of given information.
Answer to Problem 22WE
The measurement of third
Explanation of Solution
Given information:
A secant and a tangent to a
The two arcs of the circle intercepted by the secant and the tangent have measures in a ratio of 7:3.
O center is the center of the circle, where AC is a secant intersecting the circle at point B and AT is a tangent to the circle.
In the diagram we can see that,
As measure of arc CT and arc BT are in ratio 7:3 and also
Assume that measure of arc CT is
As it is known that
Put the values
Solving the above equation:
Thus measure of arc CT is
Thus measure of arc BT is
As it is known that
So put the value
Solve the equation to get
Hence, the measurement of third angle is
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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