Question 10 - End-of-Chapter Exercises - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
Last updated at May 26, 2026 by Teachoo
End-of-Chapter Exercises
Question 1
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Class 9
Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
- Definitions
- Symmetries of Circle
- Number of Circles
- Exercise Set 5.1
- Think, Draw and Infer (Page 98)
- Angle Subtended by Chords
- Exercise Set 5.2
- Mid-points and Perpendicular Bisectors of Chords
- Exercise Set 5.3
- Distance of Chords from the Centre
- Exercise Set 5.4
- Distance of unequal chords from center
- Exercise Set 5.5
- Angle subtended by an arc
- Exercise Set 5.6
- Concyclicity of Points and Cyclic Quadrilateral
- Theorems (and their Proofs)
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End-of-Chapter Exercises
Transcript
Question 10 A cyclic quadrilateral has sides 5, 5, 12, 12 units Find its area. Depending on the order of the sides, this shape is either a Rectangle (5, 12, 5, 12) or a Kite (5, 5, 12, 12) Let’s do both cases Cyclic quadrilateral is a Rectangle Since it is a rectangle Area of rectangle = Length × Breadth = 12 × 5 = 60 square units Cyclic quadrilateral is a Kite In a cyclic quadrilateral, opposite angles sum to 180°. In a kite, one pair of opposite angles are equal by symmetry. Thus, x + x = 180° 2x = 180° x = 90° So, this means the kite is made of two identical right-angled triangles joined at their hypotenuse. Area of one right triangle = ½ × 5 × 12 = 30 Thus, Total area = 30 + 30 = 60 square units Therefore, Regardless of the side arrangement, the area of the cyclic quadrilateral is 60 square units.
