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ICSE Class 9 Answered

AB is a line segment whose midpoint is M. Taking AM, BM and AB as diameters three semi-circles are drawn on the same side of AB. A circle is drawn with radius 'r' touching all the three semi-circles. Prove that r=AB/6
Asked by abhishekabin12306 | 03 Jan, 2018, 08:01: PM
answered-by-expert Expert Answer
The image will be as shown below:
 
 
begin mathsize 16px style Since space straight M space is space the space mid minus point space of space AB comma AM equals MB equals AB over 2 Since space straight P space and space straight S space are space the space midpoints space of space AM space and space MB comma AP equals PM equals MS equals SB equals AB over 4 Radius space of space straight a space circle equals straight r rightwards double arrow CP equals left parenthesis straight r plus PQ right parenthesis equals open parentheses straight r plus AB over 4 close parentheses space cm CM equals DM minus DC equals open parentheses AB over 2 minus straight r close parentheses space cm In space triangle CMP comma space angle CMP equals 90 degree rightwards double arrow CM squared plus MP squared equals CP squared rightwards double arrow open parentheses AB over 2 minus straight r close parentheses squared plus open parentheses AB over 4 close parentheses squared equals open parentheses straight r plus AB over 4 close parentheses squared Solving comma space we space get straight r equals AB over 6 end style
Answered by Rashmi Khot | 05 Jan, 2018, 10:22: AM

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AB is a line segment whose midpoint is M. Taking AM, BM and AB as diameters three semi-circles are drawn on the same side of AB. A circle is drawn with radius 'r' touching all the three semi-circles. Prove that r=AB/6
Asked by abhishekabin12306 | 03 Jan, 2018, 08:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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