Answer: AC × BD = AB × CD + AD × BC.
- A AC × BD = AB × CD + AD × BC
- B AC + BD = AB + CD, an additive but incorrect form
- C AC/BD = AB/CD, a ratio form that does not hold generally
- D AC × BD = AB × AD, missing the CD term from the product
Correct answer: A. AC × BD = AB × CD + AD × BC
Explanation: For a cyclic quadrilateral, Ptolemy proved: product of diagonals = sum of products of opposite side pairs. Diagonal AC, BD; sides AB,CD and AD,BC: AC×BD=AB×CD+AD×BC. Verified for a rectangle (special case). Ans: AC×BD=AB×CD+AD×BC.
Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.
Concept context
Perimeters, areas, and volumes of 2D and 3D shapes