JKLM is a cyclic quadrilateral in which ∠K is opposite to ∠M. When JK and ML are produced, meet at point Z. JK = 10 cm, KZ = 12 cm and MZ = 33 cm. What is the length of LZ ?

9 cm 8 cm 10 cm  12 cm

8 cm

If chords AB and CD of a circle intersect each other at a point P outside the circle then, PA × PB = PC × PD Here, ZK × ZJ = ZL × ZM ZL = 12 × \(\frac{22}{22}\)  ZL = 8 cm.