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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

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