Q19(b). Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

∠AOB+∠COD=180° and ∠BOC+∠AOD=180°, so opposite sides of the circumscribing quadrilateral subtend supplementary angles at the centre. Hence proved.

CBSE Class 10 Maths (Standard) 2019 — Paper 30/3/1

80 marks · 3 hours · 30 questions (41 with the OR choices)

6 of its 41 questions have been set in other papers too (each one says where); the other 35 are only in this paper.

Take this paper as a timed mock

Free with an account: the board's time limit, marking at the end, and the answer to every question.

Questions 1–6 · 1 mark each

Q1 1 mark

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Q2(a) 1 mark

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Q2(b) 1 mark

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Q3 1 mark

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Q4 1 mark

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Q5 1 mark

Also in 2015 · 30/2/1 (Q4)

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Q6(a) 1 mark

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Q6(b) 1 mark

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Questions 7–12 · 2 marks each

Q7(a) 2 marks

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Q7(b) 2 marks

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Q8 2 marks

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Q9(a) 2 marks

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Q9(b) 2 marks

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Q10 2 marks

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Q11 2 marks

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Q12 2 marks

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Questions 13–22 · 3 marks each

Q13(a) 3 marks

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Q13(b) 3 marks

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Q14 3 marks

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Q15 3 marks

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Q16 3 marks

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Q17(a) 3 marks

Also in 2026 · 30/1/1 (Q26), 2025 · 30/2/1 (Q30), 2025 · 30/5/1 (Q26(a)), 2025 · 430/1/1 (Q26(a)), 2025 · 430/4/1 (Q28), 2024 · 30/5/1 (Q26(a)), 2024 · 30(B) (Q26), 2023 · 30/5/1 (Q26(a)), 2023 · 30(B)/5 (Q26), 2020 · 430/2/1 (Q31(a)), 30(B) (Q16)

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Q17(b) 3 marks

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Q18(a) 3 marks

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Q18(b) 3 marks

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Q19(a) 3 marks

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Q19(b) 3 marks

Also in 2025 · 30/1/1 (Q26(b)), 2024 · 430/4/1 (Q27(a)), 2023 · 30/C/B (Q33(a))

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Show answer

$∠ A O B + ∠ C O D = 18 0^{\circ}$ and $∠ B O C + ∠ A O D = 18 0^{\circ}$ , so opposite sides of the circumscribing quadrilateral subtend supplementary angles at the centre. Hence proved.

Step-by-step solution →
Q20 3 marks

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Q21 3 marks

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Q22 3 marks

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Questions 23–30 · 4 marks each

Q23 4 marks

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Q24(a) 4 marks

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Q24(b) 4 marks

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Q25 4 marks

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Q26(a) 4 marks

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Q26(b) 4 marks

Also in 2016 · 30/1/1 (Q31)

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Q27(a) 4 marks

Also in 2023 · 430(B) (Q33)

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Q27(b) 4 marks

Also in 2020 · 430/1/1 (Q32)

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Q28 4 marks

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Q29 4 marks

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Q30 4 marks

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Other 2019 papers

All CBSE Class 10 Maths papers →