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ICSE Class 10 Answered

AB=8 cm and M is the mid-point of AB. Semicircles are drawn on AB,AM and Mb as diametrs.A circle with centre C touches all the three circles. Find the radius of circle C.
Asked by dwivedi_anand | 21 Nov, 2018, 11:48: AM
answered-by-expert Expert Answer
As shown in figure, a circle with centre C is touching the semi-circles drawn on diameters AB, AM and BM.
 
In the ΔCDM as shown in figure, CD2  = CM2 + DM2
 
CD = (1+r) cm , CM = (2 - r ) cm , DM = 1 cm
 
(1+r)2 = (2-r)2 + 12 ...............(1)

By solving the above eqn.(1), we get r = (2/3) cm
Answered by Thiyagarajan K | 22 Nov, 2018, 10:42: PM

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