Question 18 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Standard [Term I] - Solutions of Sample Papers for Class 10 Boards

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Question 18 The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 41 cm from the centre of the circle is (A) 40 cm (B) 9 cm (C) 41 cm (D) 50 cmSince AB is tangent And, we know that Tangent at any point of circle is perpendicular to the radius through point of contact Hence, OB ⊥ AB ∴ ∠ OBA = 90° So, Δ OAB is a right triangle In right triangle OAB Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 OA2 = OB2 + AB2 412 = 92 + AB2 1681 = 81 + AB2 1681 – 81 = AB2 AB2 = 1681 – 81 AB2 = 1600 AB2 = 16 × 100 AB2 = 42 × 102 AB2 = (4 × 10)2 AB2 = (40)2 AB = √(40^2 ) AB = 40 Hence, Length of Tangent = 40 cm So, correct answer is (a)