Mathematics
In the figure (i) given below, AB = 8 cm and M is mid-point of AB. Semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all three semicircles as shown, find its radius.
Circles
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Answer
Let x be the radius of the circle with centre C.
Since M is the mid-point of AB hence, AM = MB = 4 cm.
Two semicircles are thus drawn on AB with diameters as AM and MB.
Since radius = .
Hence, radius of both the semicircles with diameters AM and MB = 2 cm.
From figure,
CM = MP - PC = (4 - x) cm.
In right angled triangle CMD,
Hence, the radius of small circle = cm.
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