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Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If DBC=70,BAC is 30, find BCD . Further, if AB = BC, find ECD. [2 Marks]

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Solution

Given
DBC=70,BAC=30
For chord CD,
CBD=CAD (Angles in the same segment)CAD=70
BAD=BAC+CAD=30+70=100
BCD+BAD=180 (Opposite angles of a cyclic quadrilateral)
BCD+100=180
BCD=80 [1 Mark]
In ΔABC,
AB = BC (Given)
BCA=CAB (Angles opposite to equal sides of a triangle)
BCA=30
We have, BCD=80
BCA+ACD=80
30+ACD=80
ACD=50
ECD=50 [1 Mark]

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