abcd is a cyclic quadrilateral within a circle centre o if obc=55 and bc=cd find bad - Maths - Circles

Question

abcd is a cyclic quadrilateral within a circle centre o if
<obc=55 and bc=cd find <bad

Ashwini Kumar · Accepted Answer

Dear Student,

Please find below the solution to the asked query:
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"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5635a5c3ae512%20jpg"
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In △OBC,OB=OC⇒∠OCB=∠OBC=55°Now,∠OCB+∠OBC+∠BOC=180°⇒55°+55°+∠BOC=180°⇒∠BOC=70°We know that equal chords of a circle subtend equal angles at the centre∴∠COD=∠BOC=70°In △OCD,OC=OD⇒∠OCD=∠ODCAnd∠OCD+∠ODC+∠COD=180°⇒∠OCD+∠OCD+70°=180°⇒2∠OCD=110°⇒∠OCD=55°∴∠BCD=∠OCB+∠OCD=55°+55°=110°Again we know that opposite angles of cyclic quadrilateral are supplementary angles
∴∠BCD+∠BAD=180°⇒110°+∠BAD=180°Hence, ∠BAD=70°

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abcd is a cyclic quadrilateral within a circle centre o. if <obc=55 and bc=cd find <bad