Question 10 - 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 10 O is the point of intersection of two chords 𝐴𝐵 and 𝐶𝐷 of a circle If ∠𝐵𝑂𝐶=80^∘ and 𝑂𝐴=𝑂𝐷 then △𝑂𝐷𝐴 and △𝑂𝐵𝐶 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 Δ ODA & Δ OBC ∠ AOD = ∠ COB ∠ ODA = ∠ OBC ∴ Δ ODA ~ Δ OBC Since triangles are similar, their sides are proportional 𝑂𝐴/𝑂𝐶=𝑂𝐷/𝑂𝐵=𝐴𝐷/𝐶𝐵 For 𝑶𝑨/𝑶𝑪=𝑶𝑫/𝑶𝑩 Putting OD = OA (From (1)) (From (2)) (AA similarity) 𝑶𝑨/𝑶𝑪=𝑶𝑨/𝑶𝑩 OC = OB Thus, in Δ OBC Two sides are equal, so it is isosceles Also, in Δ ODA Given OA = OD, two sides are equal, so it is isosceles Hence, Δ ODA & Δ OBC are Isosceles Similar So, the correct answer is (B)

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