NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.5 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Perpendicular bisector

Give Perpendicular Bisector at Triangle ABC , D is a Mid Poin …

To find this point, you will construct three perpendicular bisectors, one for each side of the triangle. The point where all three perpendicular bisectors intersect is called the Circumcenter. Using this center point, we can draw a circle that passes through all three vertices.

1. ABC is a triangle. Locate a point the interior of which is equidistant from all the vertices of

Solution:

Interior of Triangle ABC
  • Draw perpendicular bisectors PQ and ₹ of sides AB and BC respectively of triangle ABC. Let PQ bisects AB at M and ₹ bisects BC at point N.
  • Let PQ and ₹ intersect at point O. Join OA, OB and OC.
  • Now in

[By construction]

[By construction]

[Common]

[By SAS congruency]

[By Coorresponding Parts of Congruent Triangles] … equation (1)

  • Similarly,

[By Corresponding Parts of Congruent Triangles.] … equation (2)

  • From eq. (1) and (2) ,

  • Hence O, the point of intersection of perpendicular bisectors of any two sides of equidistant from its vertices.