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Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If DBC=70,BAC is 30 and AB = BC, find ECD.


Solution


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
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

Mathematics
DUMMY
Standard IX

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