To show: An angle inscribed in a semicircles is right angle. .
Given data: The angle inscribed in a semicircle of radius r is shown in Fig.1.
Method/Formula used:
The product of two perpendicular lines is -1. The slope m of line passing through points
And distance d between points
Calculations:
The angle
Let coordinates of points A , B , C with respect to origin O are
Using result (1), taking points
Using result (1), taking points
The product of slopes
Now, the distance
Substitute
Therefore, lines BC and BA are perpendicular, i.e.
Thus, an angle inscribed in a semicircles is right angle.
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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