BC is the arc of a circle of radius 8 cm . a semi - circle is described on the chord BC on the side opposite to the centre of the quadrant . Find the area between arc BC and the semi circle .
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Answer:
Draw RM⊥AB
AM=MB=
2
AB
=18 cm
AP=PM=MQ=QB=
2
18
=9 cm
MR=AM=18㎝
CM=RM−CR=18−r
PC=PE+EC=9+r
In triangle CMP
PC
2
=CM
2
+PM
2
⇒(9+r)
2
=(18−r)
2
+9
2
⇒81+18r+r
2
=324−36r+r
2
+81⇒54r=324⇒r=6 cm
∴Area of shaded region=area of semi circle AB−2 area of semi circle-area of circle with C as centre
=
2
1
π×18
2
−2×
2
1
×π×9
2
−π×6
2
=162π−81π−36π=45π cm
2
Step-by-step explanation:
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