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

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

Circles

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KnowledgeBoat · Accepted Answer

Given, O is the centre of two concentric circles of radii OA = 6 cm and OB = 4 cm. PA and PB are the two tangents to the outer and inner circles respectively and PA = 10 cm. We know that, The tangent at any point of a circle and the radius through this point are perpendicular to each other. ∠OAP = ∠OBP = 90° Since, OAP is a right angled triangle, ∴ OP2 = OA2 + PA2 [By pythagoras theorem] ⇒ OP2 = 62 + 102 ⇒ OP2 = 36 + 100 ⇒ OP2 = 136 ⇒ OP = Since, OBP is a right angled triangle, ⇒ OP2 = OB2 + PB2 ⇒ PB2 = OP2 - OB2 ⇒ PB2 = ⇒ PB2 = 136 - 16 ⇒ PB2 = 120 ⇒ PB = ⇒ PB = 10.95 cm Hence, length of PB is 10.95 cm.

Mathematics

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

Circles

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