In a quadrilateral ABCD, the diagonals intersect at O. Let the area of the triangle ABD be p. If AO : OC = m : n, then what is the area of the triangle BCD ?
- A. \frac{np}{m} ✓
- B. \frac{mp}{n}
- C. \frac{n^2 p}{m^2}
- D. \frac{m^2 p}{n^2}
Correct Answer: A. \frac{np}{m}
Explanation
The triangles ABD and BCD share the same base BD. The ratio of their heights from A and C respectively to BD is equal to the ratio of their segments AO : OC = m : n. Thus, Area(BCD) = \frac{n}{m} \times Area(ABD) = \frac{np}{m}.
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