6. A B C D is a cylic Quadrilateral whose diagonals
AC & BD intersect at the untre of the ole
passing
through the vertices A, B, C &0. What is the particular
shape of the quadrilateral?
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For chord CD,
∠CBD=∠CAD ...Angles in 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 △ABC
AB=BC (given)
∠BCA=∠CAB ...Angles opposite to equal sides of a triangle
∠BCA=30°
Also, ∠BCD=80°
∠BCA+∠ACD=80°
⇒30°+∠ACD=80°
∠ACD=50°
∠ECD=50°
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