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CBSE Class 10 Answered

in fig 15.95 ab = 36 cm and m is mid point of ab semicircles are drawn on ab am mb as diameters a circle with centre c touches all the three circles find the area of shaded region
Asked by Girdhar | 21 Jan, 2018, 12:43: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight r space be space the space radius space of space the space circle space equals space CN AM equals MB space space space space space space space space space space space space space space space space space space space space space CM perpendicular MB AB equals 36 space cm TZ equals ZY 1 fourth AB equals 1 fourth cross times 36 equals 9 space cm straight r plus AB over 4 equals straight r plus 9 equals ZY In space increment ZXY space is space isosceles space triangle straight M space is space midpoint space of space AB ZM perpendicular XY ZM equals MC minus CR 1 half cross times 36 minus straight r equals 18 minus straight r In space increment ZMX Pythagoras ZM squared plus MX squared equals XZ squared 9 squared plus open parentheses 18 minus straight r close parentheses squared equals left parenthesis 9 plus straight r right parenthesis squared Solving space this space we space get space straight r equals 6 space cm straight R space be space the space radius space of space big space semicircle straight r space be space the space radius space of space two space semicircle straight r subscript 1 space be space the space radius space of space circle space inside space semicircle. shaded space area equals space Area space of space semicircle space ABC space minus space Area space of space AMT space minus space Area space of space semicircle space MBZ minus Area space of space circle space CTZ equals πR squared over 2 minus πr squared over 2 minus πr squared over 2 minus πr subscript 1 squared space space space space space space space space space space space equals fraction numerator straight pi 18 squared over denominator 2 end fraction minus fraction numerator straight pi 9 squared over denominator 2 end fraction minus fraction numerator straight pi 9 squared over denominator 2 end fraction minus straight pi 6 squared equals 45 straight pi space cm squared end style
Answered by Sneha shidid | 22 Jan, 2018, 10:04: AM

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CBSE 10 - Maths
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