Z 1 {\displaystyle Z_{1}} is an arbitrary point on k 1 {\displaystyle k_{1}} being different from P {\displaystyle P} and Q {\displaystyle Q} . The lines Z 1 P {\displaystyle Z_{1}P} and Z 1 Q {\displaystyle Z_{1}Q} intersect the circle k 2 {\displaystyle k_{2}} in P 1 {\displaystyle P_{1}} and Q 1 {\displaystyle Q_{1}} . The constant chord theorem then states that the length of the chord P 1 Q 1 {\displaystyle P_{1}Q_{1}} in k 2 {\displaystyle k_{2}} does not depend on the location of Z 1 {\displaystyle Z_{1}} on k 1 {\displaystyle k_{1}} , in other words the length is constant.