Q24. Prove that the lengths of tangents drawn from an external point to a circle are equal.

In right triangles OQP and ORP: OQ = OR (radii), OP is common and ∠OQP = ∠ORP = 90°, so △OQP ≅ △ORP by RHS; hence PQ = PR by CPCT, i.e. the tangents drawn from an external point to a circle are equal in length.

CBSE Class 10 Maths (Standard) 2017 — Paper 30(B)

90 marks · 3 hours · 31 questions

2 of its 31 questions have been set in other papers too (each one says where); the other 29 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 1–4 · 1 mark each

Q1 1 mark

This question is in the full bank. Sign up free to see it.
Q2 1 mark

This question is in the full bank. Sign up free to see it.
Q3 1 mark

This question is in the full bank. Sign up free to see it.
Q4 1 mark

This question is in the full bank. Sign up free to see it.

Questions 5–10 · 2 marks each

Q5 2 marks

This question is in the full bank. Sign up free to see it.
Q6 2 marks

This question is in the full bank. Sign up free to see it.
Q7 2 marks

This question is in the full bank. Sign up free to see it.
Q8 2 marks

This question is in the full bank. Sign up free to see it.
Q9 2 marks

Also in 2026 · 430(B) (Q29(b)), 2023 · 430(B) (Q23(b))

This question is in the full bank. Sign up free to see it.
Q10 2 marks

This question is in the full bank. Sign up free to see it.

Questions 11–20 · 3 marks each

Q11 3 marks

This question is in the full bank. Sign up free to see it.
Q12 3 marks

This question is in the full bank. Sign up free to see it.
Q13 3 marks

This question is in the full bank. Sign up free to see it.
Q14 3 marks

This question is in the full bank. Sign up free to see it.
Q15 3 marks

This question is in the full bank. Sign up free to see it.
Q16 3 marks

This question is in the full bank. Sign up free to see it.
Q17 3 marks

This question is in the full bank. Sign up free to see it.
Q18 3 marks

This question is in the full bank. Sign up free to see it.
Q19 3 marks

This question is in the full bank. Sign up free to see it.
Q20 3 marks

This question is in the full bank. Sign up free to see it.

Questions 21–31 · 4 marks each

Q21 4 marks

This question is in the full bank. Sign up free to see it.
Q22 4 marks

This question is in the full bank. Sign up free to see it.
Q23 4 marks

This question is in the full bank. Sign up free to see it.
Q24 4 marks

Also in 2026 · 30/2/1 (Q29(a)), 2026 · 430/1/1 (Q30), 2024 · 430(B)/S (Q32), 2023 · 430/4/1 (Q31(a)), 2020 · 430(B) (Q37(a)), 2018 · 30/1/1 (Q18), 2018 · 30/2/1 (Q15), 2018 · 30/3/1 (Q16), 30/1/1 (Q22), 530/1 (Q24), 2016 · 30/1/1 (Q22), 2016 · 30/2/1 (Q22), 2016 · 30(B) (Q24), 2016 · 530/1 (Q24), 2015 · 30(B) (Q24)

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Show answer

In right triangles $O QP$ and $O R P$ : $O Q = O R$ (radii), $O P$ is common and $∠ O QP = ∠ O R P = 9 0^{\circ}$ , so $△ O QP ≅ △ O R P$ by RHS; hence $P Q = P R$ by CPCT, i.e. the tangents drawn from an external point to a circle are equal in length.

Step-by-step solution →
Q25 4 marks

This question is in the full bank. Sign up free to see it.
Q26 4 marks

This question is in the full bank. Sign up free to see it.
Q27 4 marks

This question is in the full bank. Sign up free to see it.
Q28 4 marks

This question is in the full bank. Sign up free to see it.
Q29 4 marks

This question is in the full bank. Sign up free to see it.
Q30 4 marks

This question is in the full bank. Sign up free to see it.
Q31 4 marks

This question is in the full bank. Sign up free to see it.

Other 2017 papers

All CBSE Class 10 Maths papers →