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