Ex 9.3, 5 - Chapter 9 Class 9 Circles

Transcript

Ex 9.3, 5 In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC. Since BD is a line ∠ BEC + ∠ DEC = 180° 130° + ∠ DEC = 180° ∠ DEC = 180° – 130° ∠ DEC = 50° In Δ DEC ∠ DEC + ∠ EDC + ∠ ECD = 180° 50° + ∠ EDC + 20° = 180° 70° + ∠ EDC = 180° ∠ EDC = 180° – 70° ∠ EDC = 110° For segment BADCB, ∠ BAC & ∠ BDC are in the same segment So, they must be equal ∴ ∠ BAC = ∠ BDC ∠ BAC = 110°