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CGP EDU Academic Team
Published on: August 14, 2026
In the figure PQ, PO 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 PQ = 24 units and the area of the circle C 4 is A sq. units, then the value of 
is equal to (here, PO 1 = O 1 Q)
Text Solution
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CHECK THE SOLUTION.
0.5
Let the point of contact of C 4 &C 1 is A, center of C 4 is O 4 & radius is equal to r
AO 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 + 36
36r = 144 
r = 4 
A = 16 
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