An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th

An amusement fair was organised in a circular park for the children of slum clusters. Free food was supplied to them at 4 stalls situated at A, B, C and D as shown in the given figure. -Maths 9th
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(i) From figure , it is clear that angle between the lines joining stalls C,D and stalls C, B is ∠BCD . Given, ∠DBC = 60°  and ∠BAC = 40° CD is a chord of circle. Here, ∠CBD and ∠CAD  are angles in the same segment of the circle. ∴ ∠CAD = ∠CBD = 60° Now, ∠BAD = ∠BAC + ∠CAD = 40° + 60° =100°  Since, ABCD is a cyclic quadrilateral. ∠BAD + ∠BCD =180° ⇒ 100° + ∠BCD =180° ⇒ ∠BCD =180°-100° ⇒  ∠BCD = 80° Hence, angle between the lines joining stalls C, D and stalls C, B is 80°. (ii) Yes, such activities are helpful for society. (iii) Other social issues for which such compaigns are required, are old age home, orphanages, etc.
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