In ΔABC, the cevians AD, BE and CF are concurrent. AF = 4 cm, FB = 3 cm, CE = 3 cm, EA = 2 cm and BC = 9 cm. Find BD and DC.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write what is given and what is to be found AD, BE and CF are concurrent. AF = 4, FB = 3, CE = 3, EA = 2 and BC = 9 (all in cm). Find BD and DC.
2 · Draw the figure ΔABC with D on BC, E on CA and F on AB. Draw AD, BE and CF meeting at one point G. Write the lengths.
3 · Write the formula or theorem Ceva's theorem: (BD/DC) × (CE/EA) × (AF/FB) = 1.
4 · Substitute
- (BD/DC) × (3/2) × (4/3) = 1
- (BD/DC) × 2 = 1, so BD/DC = 1/2
5 · Split BC in this ratio
- BD : DC = 1 : 2, so there are 3 parts
- BD = (1/3) × 9 = 3 cm
- DC = (2/3) × 9 = 6 cm
6 · Check and box the answer Check: (3/6) × (3/2) × (4/3) = 1. So BD = 3 cm and DC = 6 cm.

Scoring tip: Go round the triangle in one direction: B to D to C, C to E to A, A to F to B. Mixing up the order is the most common mistake.