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Ex 9.3, 6 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. For segment DCBAD ∠ CBD & ∠ CAD are in the same segment So, they must be equal ∴ ∠ CAD = ∠ CBD ∴ ∠ CAD = 70° Also, ∠BAD = ∠BAC + ∠CAD ∠BAD = 30° + 70° ∠BAD = 100° Now, ABCD is a cyclic quadrilateral ∠BCD + ∠BAD = 180° ∠BCD + 100° = 180° ∠BCD = 180° – 100° ∠ BCD = 80° Also, if AB = BC, we need to find ∠ ECD In ∆ ABC, AB = BC So, ∠ BCA = ∠ BAC ∴ ∠ BCA = 30° Also, ∠ BCD = ∠ BCA + ∠ ECD 80° = 30° + ∠ ECD ∠ ECD = 80° – 30° ∠ ECD = 50°

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo