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O is the center of the sector OAB. CD is another arc, with center O and radius r cm. DB = 2cm. If the area of ABDC is one-third the area of the sector OCD find the value of r ?
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Pure Math (As) , Help :(
- Thread starter GorgeousEyes
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Radius of CD=r and so radius of OB=r-2
area of ABDC=1/3 area of OCD
1/2(r square x Theta-(r-2)square x theta)= 1/3 r Sq x Theta
1/2(r(sq) theta -(r-2) sq Theta)=1/3 r(sq) Theta
2r(sq)=3(( r(sq)-(r-2)sq)) simplifying it
r(sq) -6r+ 6=0
solve for r using quadratic formula you get
r=3 +sq.rt(3)
area of ABDC=1/3 area of OCD
1/2(r square x Theta-(r-2)square x theta)= 1/3 r Sq x Theta
1/2(r(sq) theta -(r-2) sq Theta)=1/3 r(sq) Theta
2r(sq)=3(( r(sq)-(r-2)sq)) simplifying it
r(sq) -6r+ 6=0
solve for r using quadratic formula you get
r=3 +sq.rt(3)