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NTA Abhyas JEE Main2020MathematicsCirclePractice

In the figure P Q ,   P O 1 and O 1 Q are the diameters of semicircles C 1 ,   C 2 and C 3 with centres at O 1 ,   O 2 and O 3 respectively and the circle C 4 touches the semicircles C 1 , C 2 and C 3 . If P Q = 24 units and the area of the circle C 4 is A sq. units, then the value of 8 π A is equal to here ,   P O 1 = O 1 Q

Correct answer

0.5

Step-by-step solution

Let the point of contact of C 4 & C 1 is A , center of C 4 is O 4 & radius is equal to r ⇒ A O 1 = 12 ⇒ O 1 O 4 = 12 - r Also, O 4 O 3 = r + 6 and O 1 O 3 = 6 ⇒ r + 6 2 = 12 - r 2 + 3 6 ⇒ 36 r = 144 ⇒ r = 4 ⇒ A = 16 π ⇒ 8 π A = 8 π 16 π = 1 2 = 0 . 5

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