Question

In the given figure, O is the centre of two concentric circles of radii 4 cm and 6cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10cm, find the length of PB up to one place of decimal.

Answer 1

Consider ΔPOA

OA = 6 cm …radius of the outer circle

PA = 10 cm …given

∠OAP = 90° …radius is perpendicular to the tangent

Hence ΔPOA is right-angled triangle

Using Pythagoras

⇒ OA² + AP² = OP²

⇒ 6² + 10² = OP²

⇒ 36 + 100 = OP²

⇒ OP² = 136 …(i)

Consider ΔPBO

OB = 4 cm …radius of inner circle

∠OBP = 90° …radius is perpendicular to the tangent

Hence ΔPOB is right-angled triangle

Using Pythagoras

⇒ OB² + BP² = OP²

Using (i)

⇒ 4² + BP² = 136

⇒ 16 + BP² = 136

⇒ BP² = 120

⇒ BP = 10.9 cm

Hence length of PB is 10.9 cm