Question

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is ______ 

 

Options

• 10 cm

• 8 cm

• 6 cm

• 4 cm

Answer 1

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is 8 cm.

Explanation:

∠OAC = ∠CBP = 90°

∠OCA = ∠PCB (Vertically opposite angle)

Triangle OAC is similar to PBC

`"OA"/"PB" = "OC"/"PC"`

`3/3 = "OC"/"PC"`

OC = PC

But PO = 10 cm

Therefore OC = PC = 5cm

AC² = OC² - OA²

AC² = 5² - 3²

AC = 4 cm

Similarly BC = 4 cm

Therefore AB = 8 cm