2026 · Q53
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?
Elementary MathematicsQuadrilaterals and Polygons
- Anp/m
- Bmp/n
- Cn²p/m²
- Dm²p/n²
Explanation
ΔABD and ΔBCD share the base BD, and the heights from A and C to line BD are in the ratio AO:OC=m:n. Hence area(ΔBCD)=p·(n/m)=np/m, option A. The shared base BD cancels out, leaving only the height ratio AO:OC to scale the area.