Question : If in acute-angled triangle ABC, AL, BM, and CN are the three altitudes of triangle ABC, then which of the following statements will be true?
Option 1: AL + BM + CN = AB + BC + CA
Option 2: AL + BM = AB + BC
Option 3: AL + BM + CN > AB + BC + CA
Option 4: AL + BM + CN < AB + BC + CA
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Correct Answer: AL + BM + CN < AB + BC + CA
Solution :
We know the theorem states that the sum of three altitudes of a triangle is less than the sum of three sides of the triangle. The altitudes form right angles with the opposite sides of the triangle.
Hence, the correct answer is AL + BM + CN < AB + BC + CA.
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