CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard

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

Last updated at Oct. 3, 2024 by

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Question 10

O is the point of intersection of two chords 𝐴𝐡 and 𝐢𝐷 of a circle If ∠𝐡𝑂𝐢=80^∘ and 𝑂𝐴=𝑂𝐷 then △𝑂𝐷𝐴 and △𝑂𝐡𝐢 are

(A) equilateral and similar

(B) isosceles and similar

(C) isosceles but not similar

(D) not similar

 

 

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Question 10 O is the point of intersection of two chords 𝐴𝐡 and 𝐢𝐷 of a circle If βˆ π΅π‘‚πΆ=80^∘ and 𝑂𝐴=𝑂𝐷 then △𝑂𝐷𝐴 and △𝑂𝐡𝐢 are (A) equilateral and similar (B) isosceles and similar (C) isosceles but not similar (D) not similar Here, ∠ AOD = ∠ COB Also, ∠ ODA = ∠ OBC (Vertically opposite angles) (Angle in the same segment are equal) Now, In Ξ” ODA & Ξ” OBC ∠ AOD = ∠ COB ∠ ODA = ∠ OBC ∴ Ξ” ODA ~ Ξ” OBC Since triangles are similar, their sides are proportional 𝑂𝐴/𝑂𝐢=𝑂𝐷/𝑂𝐡=𝐴𝐷/𝐢𝐡 For 𝑢𝑨/𝑢π‘ͺ=𝑢𝑫/𝑢𝑩 Putting OD = OA (From (1)) (From (2)) (AA similarity) 𝑢𝑨/𝑢π‘ͺ=𝑢𝑨/𝑢𝑩 OC = OB Thus, in Ξ” OBC Two sides are equal, so it is isosceles Also, in Ξ” ODA Given OA = OD, two sides are equal, so it is isosceles Hence, Ξ” ODA & Ξ” OBC are Isosceles Similar So, the correct answer is (B)

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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 and Computer Science at Teachoo