In the figure, PC||QK and BC||HK. If AQ = 6 cm, QH = 4 cm, HP = 5 cm, KC = 18 cm, then find AK and PB.

Given: PC||QK and BC||HK, AQ = 6 cm, QH = 4 cm, HP = 5 cm, KC = 18 cm

Required: Length of AK and PB

Consider the ΔAPC

Here, PC||QK

∴ By Thales theorem

Here, QP = QH + HP = 4 + 5 = 9cm

⇒

⇒

∴ AK = 12cm

Now, Consider ΔABC

Here, BC||HK

∴ By Thales theorem

Here, AH = AQ + QH = 6 + 4 = 10cm

⇒

⇒

⇒ HB = 15cm

⇒ PB = HB—HP = 15—5 = 10cm

∴ PB = 10cm

∴ Length of AK and PB are 12 cm and 10 cm respectively.