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Question 11. (a) In the figure (i) given below, O is the centre of the circle. If ∠COD = 40° and ∠CBE = 100°, then find : (i) ∠ADC (ii) ∠DAC (iii) ∠ODA (iv) ∠OCA. (b) In the figure (ii) given below, O is the centre of the circle. If ∠BAD = 75° and BC = CD, find : (i) ∠BOD (ii) ∠BCD (iii) ∠BOC (iv) ∠OBD

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This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15. This question has been asked in previous year question paper of 2009

 In the figure(i) given, O is the centre of the circle. ∠COD = 40° and ∠CBE = 100°, then we have to find : (i) ∠ADC (ii) ∠DAC (iii) ∠ODA (iv) ∠OCA.

In the figure (ii) given  O is the centre of the circle.  ∠BAD = 75° and BC = CD,

Now we have to find : (i) ∠BOD (ii) ∠BCD (iii) ∠BOC (iv) ∠OBD

ICSE Avichal publication
Understanding ICSE Mathematics
Question 11

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1 Answer

  1. Solution:
    (a) (i) ∴ ABCD is a cyclic quadrilateral.
    ∴ Ext. ∠CBE = ∠ADC
    ⇒ ∠ADC = 100°
    (ii) Arc CD subtends ∠COD at the centre
    and ∠CAD at the remaining part of the circle
    ∴ ∠COD = 2 ∠CAD
    ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.2
    ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.3
    ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.4
    ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.5

     

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