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Asked: 2026-10-03T06:01:00+00:00 In:

Consider 4 points A, B, C, D in the plane with no three collinear. Answer the following questions. Some answers may require you to consider different cases, depending on how the points are positioned in the plane. (i) How many different quadrilaterals do they form if the quadrilateral is allowed to be self-intersecting or non-convex? (ii) How many of these quadrilaterals are self-intersecting? How many are convex?

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(i) Exactly 3 distinct cyclic edge orderings can be formed. (ii) If the 4 points form a convex hull: 1 is convex and 2 are self-intersecting. If 1 point is inside: 0 are convex, 3 are non-convex and 0 self-intersect.

Class 9 Ganita Manjari part 2 Chapter 12 Solutions
Class 9 Ganita Manjari Part 2 Chapter 12 Page 78 Question Answer

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    1. (i) The 4 points can be arranged cyclically in (4-1)!/2 = 3 distinct edge-connectivity cycles, giving 3 quadrilaterals. (ii) There are two cases: • Case 1 (points form a convex quadrilateral): Exactly 1 is convex and the other 2 are self-intersecting. • Case 2 (one point lies inside the triangle of the other three): None are convex; all 3 form non-convex dart shapes.

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-12/

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