In any triangle the circumcentre O, the centroid G and the orthocentre H lie on one straight line, and G divides OH so that OG : GH = 1 : 2. If OG measures 4 cm, what is the length of OH?

OG : GH = 1 : 2 with OG = 4 cm gives GH = 8 cm, and since G lies between O and H the whole segment is OH = 4 + 8 = 12 cm. The trap 8 cm answers GH, the far piece, rather than the whole; 6 cm treats G as the midpoint and doubles once too little; 16 cm adds 4 to 12 as though the ratio were 1 : 3. (The nine-point centre sits at the midpoint of OH, so it would be 6 cm from O — that is where the 6 cm comes from.)