In equilateral triangle ABC, point E lies on CA such that BE perpendicular to CA. Find AB 2 +BC 2 +CA 2 in terms of BE 2
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See the diagram.
BE ⊥ AC. In an equilateral triangle, the perpendicular from a vertex is the median. Hence AE = CE = a (say)
Let BE = x.
Pythagoras theorem => (2a)² = a² + x²
a² = 3 x² /4
LHS = AB² + BC² + CA² = 12 a² = 9 x²
BE ⊥ AC. In an equilateral triangle, the perpendicular from a vertex is the median. Hence AE = CE = a (say)
Let BE = x.
Pythagoras theorem => (2a)² = a² + x²
a² = 3 x² /4
LHS = AB² + BC² + CA² = 12 a² = 9 x²
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3
Answer: 4 BE^2
Step-by-step explanation:
Explanation is in attachment.
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