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NCERT Class 9 Mathematics Exercise Set 5.2 Solutions: I’m Up and Down, and Round and Round

AI-written, checked on 23 Oct 2026

Solutions written by Shishya, checked — not the board's official answers

Step-by-step working for every question of Exercise Set 5.2 in NCERT's Class 9 Mathematics book, chapter “I’m Up and Down, and Round and Round”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.

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How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.

Tap “why?” under a step to see the textbook rule it uses — from Shishya's fixed list of NCERT Class 9-10 rules, not written by AI for this page. A step without one has no rule from the list yet.

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  1. Ex 5.2 Q1

    Show that a chord and the centre of the circle form an isosceles triangle.

    1. Let O be the centre of the circle and AB be a chord of the circle.
    2. Join O to A and O to B.
    3. OA is a radius of the circle.
    4. OB is a radius of the circle.
    5. All radii of the same circle are equal in length.
    6. Therefore, OA = OB.
    7. In triangle OAB, two sides OA and OB are equal.
    8. A triangle with two equal sides is an isosceles triangle.
    9. Hence, the triangle formed by the chord and the centre is isosceles.

    Answer: Proved that the triangle formed by a chord and the centre of the circle is isosceles.

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  2. Ex 5.2 Q2

    Show that two such isosceles triangles (chord + centre, same circle) with equal bases are congruent.

    1. Consider two isosceles triangles formed by the center and two chords of the same circle.
    2. Let the first triangle be △OAB and the second be △OCD, where O is the center.
    3. Since OA, OB, OC, and OD are all radii of the same circle, OA = OB = OC = OD.
    4. We are given that the bases are equal, so AB = CD.
    5. In △OAB and △OCD, we have OA = OC (radii), OB = OD (radii), and AB = CD (given).
    6. By the SSS (Side-Side-Side) congruence criterion, △OAB ≅ △OCD.

    Answer: The two isosceles triangles are congruent by SSS criterion.

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