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The bisectors of angles A and B of a scalene triangle ABC meet at O. What is the point O called? OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?

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Question

The bisectors of angles A and B of a scalene triangle ABC meet at O.

  1. What is the point O called?
  2. OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
  3. What is the relation between angle ACO and angle BCO?
Sum
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Solution

 

  1. O is called the incentre of the incircle of ΔABC.
  2. OR and OQ are the radii of the incircle and OR = OQ.
  3. OC is the bisector of angle C.
    ∴ ∠ACO = ∠BCO  
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Chapter 19: Constructions (Circles) - Exercise 19 [Page 293]

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Selina Concise Mathematics [English] Class 10 ICSE
Chapter 19 Constructions (Circles)
Exercise 19 | Q 11. | Page 293

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