Question 15 - 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 15 Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals must lie at the centre of the circle. Given: A circle with center O ABCD is a rectangle inscribed in a circle with diagonals AC & BD To prove: Diagonals AC & BD intersect at center O Proof: Let’s look at diagonal AC & ∠ B Here, we have chord AC, making ∠ ABC = 90° at point B on circle Since chord AC makes a 90° angle at any point of the circle Thus, AC must be the diameter Because angle in a semi-circle is a right angle Since AC is the diameter, it must pass through center O Similarly, we can say Chrod BD makes ∠ A = 90° on the circle So, BD is the diameter, and passes through center O Thus, both diagonals AC & BD pass through center O Hence proved
