2008 iTest Problems/Problem 74
Revision as of 18:42, 21 November 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 74 -- centroids and quads)
Problem
Points and lie on opposite sides of line . Let and be the centroids of and respectively. If , , , , and , find the sum of the numerator and denominator of the value of when expressed as a fraction in lowest terms.
Solution
Notice that and , so and are right triangles. Since , quadrilateral is cyclic.
Let be the midpoint of . Since and are centroids, . Thus, by SAS Similarity, , so .
By Ptolemy's Theorem, , so
That means , and the sum of the numerator and denominator in lowest terms is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 73 |
Followed by: Problem 75 | |
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