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ICSE Class X Math 2019 Paper

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Question : 32 of 32
Marks: +1, -0
In the given figure, ABCDE\mathrm{ABCDE} is a pentagon inscribed in a circle such that AC\mathrm{AC} is a diameter and side BC∥AE\mathrm{BC} \parallel \mathrm{AE}. If ∠BAC=50∘\angle \mathrm{BAC} = 50^{\circ}, find giving reasons:
(i) ∠ACB\angle \mathrm{ACB}
(ii) ∠EDC\angle \mathrm{EDC}
(iii) ∠BEC\angle \mathrm{BEC}
Hence prove that BE\mathrm{BE} is also a diameter
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