NCERT Solutions for Class 9 Maths Chapter 10
Important NCERT Questions
Circles
NCERT Books for Session 2022-2023
CBSE Board, UP Board and Other state Boards
EXERCISE 10.5
Page No:186
Questions No:12
Prove that a cyclic parallelogram is a rectangle.
Share
Get Hindi Medium and English Medium NCERT Solution for Class 9 Maths to download.
Please follow the link to visit website for first and second term exams solutions.
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/chapter-10/
Given: Quadrilateral ABCD is a cyclic quadrilateral.
To Prove: ABCD is a rectangle.
Proof: In cyclic quadrilateral ABCD
∠A + ∠C = 180° …(1)
[∵ The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.]
But ∠A = ∠C …(2)
[∵ Opposite angles of a parallelogram are equal]
From the equation (1) and (2).
∠A + ∠A = 180°
⇒ 2∠A = 180°
⇒ ∠A = 180°/2 = 90°
We know that, a parallelogram with one angle right angle, is a rectangle.
Hence, ABCD is a rectangle.