Difference between revisions of "1985 AHSME Problems/Problem 22"
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− | In a circle with center <math> O </math>, <math> AD </math> is a [[diameter]], <math> ABC </math> is a [[chord]], <math> BO=5 </math> | + | In a circle with center <math> O </math>, <math> AD </math> is a [[diameter]], <math> ABC </math> is a [[chord]], <math> BO=5 </math> and <math> \angle ABO= \ \stackrel{\frown}{CD} \ =60^\circ </math>. Then the length of <math> BC </math> is |
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==See Also== | ==See Also== | ||
{{AHSME box|year=1985|num-b=21|num-a=23}} | {{AHSME box|year=1985|num-b=21|num-a=23}} | ||
+ | {{MAA Notice}} |
Revision as of 01:08, 3 April 2018
Problem
In a circle with center , is a diameter, is a chord, and . Then the length of is
Solution
Since is inscribed and intersects an arc of length , . Thus, is a right triangle. Thus, and . Since and are both radii, and . Since is inscribed in a semicircle, it's a right angle, and is also a right triangle. Thus, and . Finally, .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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