Ex 10.5, 6 - ABCD is a cyclic quadrilateral whose diagonals - Cyclic quadrilaterals

Ex 10.5, 6 - Chapter 10 Class 9 Circles - Part 2

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Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.