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NTA Abhyas JEE Main2020MathematicsCirclePractice

Let P and Q be 2 circles externally touching each other at point X . Line segment A B is a direct common tangent to circles P and Q at points A and B respectively. Another common tangent to P and Q at X intersects line A B at a point Y . If B Y = 10 units and the radius of P is 9 units, then the value of the reciprocal of the radius of the circle Q is equal to

Correct answer

0.09

Step-by-step solution

A Y = B Y     ( ∵ Y lies on the radical axis) From the figure, A B 2 = r 1 + r 2 2 - r 1 - r 2 2 = 4 r 1 r 2 A B = 2 r 1 r 2 Now, B Y = 10 (given) ⇒ A B = 20 = 2 9 r 2 ⇒ r 2 = 100 9 ⇒ 1 r 2 = 0 . 09

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