In the given figure, O is the centre of two concentric circles of radi

1.	In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to the outer and inner circle respectively. If PA = 10 cm, find the length of PB up to one place of decimal.
Answer» In the given figure, PA and PB are the tangents drawn from P, to the outer circle and inner circle respectively. PA = 10 cm OA and OB are the radii and PA and PB are two tangents to the circles respectively So, OA ⊥ PA and OB ⊥ PB In right ∆OAP, By Pythagoras Theorem: OP² = OA² + PA² = (6)² + (10)² OP²= 136 …(1) From right ∆OBP, OP² = OB² + PB² 136 = (4)² + PB² 136 = 16 + PB² [Using equation (1)] We have PB² = 136 – 16 = 120 Or PB = √120 cm = 2√30 cm = 2 x 5.47 = 10.9 Answer: Length of PB is 10.9 cm

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

Answer»

In the given figure,

PA and PB are the tangents drawn from P, to the outer circle and inner circle respectively.

PA = 10 cm

OA and OB are the radii and

PA and PB are two tangents to the circles respectively

So,

OA ⊥ PA and OB ⊥ PB

In right ∆OAP,

By Pythagoras Theorem:

OP² = OA² + PA²

= (6)² + (10)²

OP²= 136 …(1)

From right ∆OBP,

OP² = OB² + PB²

136 = (4)² + PB²

136 = 16 + PB²

[Using equation (1)]

We have PB² = 136 – 16 = 120

Or PB = √120 cm = 2√30 cm = 2 x 5.47 = 10.9

Answer: Length of PB is 10.9 cm

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