Maths · Co-ordinate of the centroid, orthocentre and circumcentre of a triangle
In a triangle divides BC in the ratio 3: 2 and divides in the ratio 1: 3. The li
In a triangle \( A B C, D \) divides BC in the ratio 3: 2 and \( E \) divides \( C A \) in the ratio 1: 3. The lines \( A D \) and \( B E \) meet at \( H \) and \( C H \) meets \( A B \) in \( F \). Find the ratio in which \( F \) divides AB.
- A. \( A F: F B=2: 1 \)
- B. \( A F: F B=1: 2 \)
- C. \( A F: F B=2: 3 \)
- D. \( A F: F B=3: 2 \)
Step-by-step solution
Using Ceva's theorem: (AF/FB) * (BD/DC) * (CE/EA) = 1. Given BD/DC = 3/2 and CE/EA = 1/3, substitute: (AF/FB) * (3/2) * (1/3) = 1 → (AF/FB) * (1/2) = 1 → AF/FB = 2. Therefore, AF:FB = 2:1.
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