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Ayesha Thakur
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Asked: 2020-11-05T08:47:43+00:00 In:

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

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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:185
Questions No:7

2020-2021cbsechapter 10circlesclass 9mathematicsncert
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    2 Answers

    1. 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/

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    2. Best Answer
      If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

      AC is Diameter of circle.
      Hence, ∠ADC = 90° and ∠ABC = 90° …(1) [∵ Angle in a Semicircle is a right angle.]
      Similarly, BD is Diameter of circle.
      Hence, ∠BAD = 90° and ∠BCD = 90 …(2) [∵ Angle in a semicircle is a right angle.]
      From the equation (1) and (2), ∠ADC = ∠ABC = ∠BAD = ∠BCD = 90°
      Hence, ABCD is a rectangle.

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