A small circle touches a large circle internally. The large circle has radius 15 cm and the two centres are 4 cm apart. What is the length of the longest chord of the small circle?

For internal contact the distance between the centres is the DIFFERENCE of the radii, so $15-r=4$ and $r=11$ cm. The longest chord of any circle is its diameter, so the answer is $2\times 11=22$ cm. The trap 11 cm stops at the radius and forgets that a chord was asked for; 19 cm adds the 4 cm instead of subtracting it, which is the condition for EXTERNAL contact; and 30 cm is the diameter of the large circle.