Difference between revisions of "1968 AHSME Problems/Problem 12"
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== Solution == | == Solution == | ||
− | <math>\fbox{C}</math> | + | The triangle that goes through all the vertices of the triangle is the circumcircle of the triangle. |
+ | <math>(7\frac{1}{2})^{2}+10^{2}=(12\frac{1}{2})^{2}</math>, so the triangle is a right triangle.The radius of a circumcircle | ||
+ | of a right triangle is half the hypotenuse. <math>\frac{1}{2}\cdot \frac{25}{2}=\frac{25}{4}\implies</math> <math>\fbox{C}</math> | ||
== See also == | == See also == |
Latest revision as of 20:02, 12 October 2015
Problem
A circle passes through the vertices of a triangle with side-lengths The radius of the circle is:
Solution
The triangle that goes through all the vertices of the triangle is the circumcircle of the triangle. , so the triangle is a right triangle.The radius of a circumcircle of a right triangle is half the hypotenuse.
See also
1968 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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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