Q. 114.0( 24 Votes )

In the given figure, O is the center 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 given Figure,


OA AP


[Tangent at any point on the circle is perpendicular to the radius through point of contact]


In right - angled OAP,


By Pythagoras Theorem


[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2]


(OP)2 = (OA)2 + (PA)2


Given, PA = 10 cm and OA = radius of outer circle = 6 cm


(OP)2 = (6)2 + (100)2


(OP)2 = 36 + 100 = 136 [1]


Also,


OB BP


[Tangent at any point on the circle is perpendicular to the radius through point of contact]


In right - angled OBP,


By Pythagoras Theorem


[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2]


(OP)2 = (OB)2 + (PB)2


Now, OB = radius of inner circle = 4 cm


And from [2]


(OP)2 = 136


136 = (4)2 + (PB)2


(PB)2 = 136 - 16 = 120


PB = 10.9 cm


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