Question 14 - 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 14 Show that rectangle is the only parallelogram that can be inscribed in a circle. Given: Let ABCD be a cyclic parallelogram To prove: ABCD is a rectangle Proof: A rectangle is a parallelogram with one angle 90° So, we have to prove one angle 90° We know that Opposite angles of parallelogram are equal Therefore, ∠A = ∠C Now, In cyclic parallelogram ABCD Sum of opposite angles is 180° So, we can write ∠A + ∠C = 180° Putting ∠A = ∠C from (1) ∠A + ∠A = 180° 2∠A = 180° ∠A = (180°)/2 ∠ A = 90° Thus, ABCD is a parallelogram with one angle 90° ∴ ABCD is a rectangle Hence proved
