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
ConciderΔAOB,ΔAOCandΔBOC.AB=BC=AC(Sides of equilateral triangle)AO=BO=CO(Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB(SSS congruence).∴Area ofΔAOB=Area ofΔBOC=Area ofΔAOC.ButArea ofΔAOB+Area ofΔBOC+Area ofΔAOC=Area ofΔABC.∴Area ofΔBOC=13Area ofΔABC
Hence, the given statement is true.
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:
A
ConciderΔAOB,ΔAOCandΔBOC.AB=BC=AC(Sides of equilateral triangle)AO=BO=CO(Radii of circumcircle)∴ΔAOB≅ΔBOC≅ΔCOB(SSS congruence).∴Area ofΔAOB=Area ofΔBOC=Area ofΔAOC.ButArea ofΔAOB+Area ofΔBOC+Area ofΔAOC=Area ofΔABC.∴Area ofΔBOC=13Area ofΔABC
Hence, the given statement is true.
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