Two chords AB and CD of a circle cross at a point P inside the circle. If AP = 6 cm, PB = 4 cm and CP = 3 cm, what is the length of PD?

For two chords meeting inside a circle, the products of the two parts are equal: AP × PB = CP × PD. So $6\times 4=3\times$ PD, giving 24 = 3 PD and PD = 8 cm. Pairing the wrong segments as $6\times 3=4\times$ PD would give 4.5 cm.