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

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