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In the figure O is the …

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In the figure O is the centre of the circle and angle BCO=30.Find x and y

    • Posted by Aditya Raj 5 years ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Naman Kumar 5 years ago

    Given−BA, BD & BC are the chords of the circle with centre O.AE⊥BC & OD⊥AE.∠OCE=30o.To find out−∠BAE=x=? And ∠DBC=y=? Solution−We join AD & DC.∠ABD=21​∠AOD=21​×90o=45o.(∵ The angle at the centre of a circle subtended by a chordis double of that at the circumference.).∴ In ΔOEC we have ∠COE=180o−(∠OEC+∠OCE)=180o−(90o+30o)=60o.                            (angle sum property of triangles)∴ ∠DOC=∠DOE−∠COE=90o−60o=30o.Now ∠DBC=y=21​∠DOC=21​×30o=15o.(∵ The angle at the centre of a circle subtended by a chordis double of that at the circumference.).Again ∠ABE=y+45o=45o+15o=60o.∴ In ΔABE we have ∠BAE=x=180o−(∠ABE+∠AEB)=180o−(60o+90o)=30o.                             (angle sum property of triangles)So x=30o & y=15o

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