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In triangle ABC, the medians AD and CF meet at the centroid G and are mutually perpendicular there. If BC = 3 cm and AB = 4 cm, find the length of AC (in cm).
- sqrt(5)
- sqrt(6)
- 2
- sqrt(7)
Correct answer: sqrt(5)
Solution
A standard result: if the medians from vertices A and C are perpendicular, then b² (the side AC) satisfies AB² + BC² = 5*AC². Substitute the given lengths.
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