CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at Oct. 3, 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)
