Question 7 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 17, 2024 by Teachoo

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Question 7 In the given figure, a tangent has been drawn at a point 𝑃 on the circle centred at 𝑂. If ∠TPQ=110^∘ then ∠POQ is equal to (A) 110^∘ (B)70^∘ (C) 140^∘ (D) 55^∘We need to find ∠POQ We know that Tangent at any point in the circle is perpendicular to radius at the point of contact So, PT ⊥ OP ∴ ∠ OPT = 90° Now, ∠OPT = ∠QPT + ∠QPO 110° = 90° + ∠QPO ∴ ∠QPO = 20° Also, Since OP = OQ ∴ ∠QPO = ∠PQO So, ∠QPO = ∠PQO = 20° In △P𝑂𝑄 ∠QPO + ∠POQ + ∠PQO = 180° (Both are radius) (Angles opposite to equal sides are equal) 20° + ∠POQ + 20 ° = 180° ∠POQ = 180° – 40° ∠POQ = 140° So, the correct answer is (C)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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