1951 AHSME Problems/Problem 46
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Problem
is a fixed diameter of a circle whose center is . From , any point on the circle, a chord is drawn perpendicular to . Then, as moves over a semicircle, the bisector of angle cuts the circle in a point that always:
Solution
Draw in diameter . Note that, as it is inscribed in a semicircle, always has a right angle at . Since it is given that , by congruent corresponding angles. bisects , as well as the arc subtended by , . Because , always .
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 45 |
Followed by Problem 47 | |
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