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Ayesha Thakur
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Asked: 2020-11-05T08:47:33+00:00 In:

. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

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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:186
Questions No:10

2020-2021cbsechapter 10circlesclass 9mathematicsncert
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    1. Best Answer
      . If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

      Construction: Join AD.
      Proof: AB is diameter of circle and ∠ADB is Formed in semi-circle.
      Hence, ∠ADB = 90° …(1) [∵ Angle in a semicircle is a right angle]
      Similarly, AC is diametar and ∠ADC is formed in semi- circle.
      Hence, ∠ADC = 90° …(2) [∵ Angle in a semicircle is a right angle]
      Here, ∠ADB + ∠ADC = 90° + 90° = 180°
      ∠ADB and ∠ADC are forming linear pair. Therefore BDC is a straight line.
      Hence, the point D lies on third side BC.

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    2. 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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