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Example 4 - In figure, ABCD is a cyclic quadrilateral - Cyclic quadrilaterals

  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Transcript

Example 4 In figure , ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠ DBC = 55° and ∠ BAC = 45°, find ∠ BCD. For segment DABCD ∠ DAC & ∠ DBC are in same segment, so they will be equal ∴ ∠ DAC = ∠ DBC = 55° Now, ∠BAD = ∠ DAC + ∠ BAC = 55° + 45° = 100° Now, in cyclic quadrilateral ABCD ∠ BAD + ∠ BCD = 180° 100° + ∠ BCD = 180° ∠ BCD = 180° – 100° ∠ BCD = 80°

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