Question
In the given figure, ΔABC is equilateral with point O as its circumcentre. Here, area of ΔBOC=13 area of ΔABC.
Answer: Option A
:
A
Concider ΔAOB,ΔAOC and ΔBOC.AB=BC=AC (Sides of equilateral triangle)AO=BO=CO (Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB (SSS congruence).∴Area of ΔAOB=Area of ΔBOC=Area of ΔAOC.But Area of ΔAOB+Area of ΔBOC+Area of ΔAOC=Area ofΔABC.∴Area of ΔBOC=13Area of ΔABC
Hence, the given statement is true.
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:
A
Concider ΔAOB,ΔAOC and ΔBOC.AB=BC=AC (Sides of equilateral triangle)AO=BO=CO (Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB (SSS congruence).∴Area of ΔAOB=Area of ΔBOC=Area of ΔAOC.But Area of ΔAOB+Area of ΔBOC+Area of ΔAOC=Area ofΔABC.∴Area of ΔBOC=13Area of ΔABC
Hence, the given statement is true.
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