Question 11 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards

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Question 11 In the figure given below, radius r of the circle which touches the sides of the triangle is (A) 3 cm (B) 6 cm (C) 7 cm (D) 4 cmWe know that Tangent is perpendicular to the radius, ∴ OD ⊥ BC & OE ⊥ AC In quadrilateral OECD ∠ C = 90° and ∠ OEC = ∠ ODC = 90° So, 4th angle will also be 90° And, adjacent sides are equal Since all angles are 90° and adjacent sides are equal It means all sides will be equal ∴ OECD is a square Thus, we can say EC = CD = r So, we can write AE = 24 – r BD = 7 – r Also, From Theorem 10.2, lengths of tangents drawn from external point are equal Hence, AF = AE = 24 – r BF = BD = 7 – r CD = CE = r Now, AB = AF + BF 25 = (24 – r) + (7 – r) 25 = 24 + 7 – r – r 25 = 31 – 2r 2r = 31 – 25 2r = 6 r = 6/2 r = 3 Thus, radius of circle = 3 cm So, the correct answer is (a)