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Daniel

An equilateral triangle of side 9 cm​

answers: 1
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Answer:

△ABC is an equilateral triangle

AB=BC=CA=9cm

O is the circumcentre of △ABC

∴OD id the perpendicular of the side BC

In △OBD and △ODC

OB=OC  (Radius of the circle)

BD=DC  (D is the mid point of BC)

OD=OD  (common)

∴△OBD=△ODC

⇒∠BOD=∠COD

∠BOC=2∠BAC=2×60  

∘  =120  

(The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle)

∴∠BOD=∠COD=  2

∠BOC  =  2

120    =60  

BD=BC=  2

BC  =  29cm

In △BOD

⇒sin∠BOD=sin60  

=  OB, BD

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Laura Rogers
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