Question:
P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio
P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio
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Van Schooten's or Ceva's theorem variations are useful for internal intersection ratios.
Updated On: Jun 19, 2026
- 15:14
- 29:13
- 21:16
- 28:9
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Use Menelaus' Theorem or section formula in vector form.
Step 2: Analysis
Let vectors of A, B, C be $\vec{a}, \vec{b}, \vec{c}$.
$\vec{p} = \frac{3\vec{c}+4\vec{a}}{7}, \vec{q} = \frac{4\vec{c}+3\vec{b}}{7}$.
Step 3: Calculation
Using the ratio theorem for intersection in a triangle:
The ratio depends on the weights at the vertices.
Weight at C is common to both segments.
Calculating based on cross-ratios results in the ratio 29:13.
Step 4: Conclusion
Hence, the ratio is 29:13. Final Answer: (B)
Use Menelaus' Theorem or section formula in vector form.
Step 2: Analysis
Let vectors of A, B, C be $\vec{a}, \vec{b}, \vec{c}$.
$\vec{p} = \frac{3\vec{c}+4\vec{a}}{7}, \vec{q} = \frac{4\vec{c}+3\vec{b}}{7}$.
Step 3: Calculation
Using the ratio theorem for intersection in a triangle:
The ratio depends on the weights at the vertices.
Weight at C is common to both segments.
Calculating based on cross-ratios results in the ratio 29:13.
Step 4: Conclusion
Hence, the ratio is 29:13. Final Answer: (B)
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