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:
![ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.2](https://www.learninsta.com/wp-content/uploads/2018/08/ML-Aggarwal-Class-10-Solutions-for-ICSE-Maths-Chapter-15-Circles-Ex-15.2-Q11.2.png)
![ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.3](https://www.learninsta.com/wp-content/uploads/2018/08/ML-Aggarwal-Class-10-Solutions-for-ICSE-Maths-Chapter-15-Circles-Ex-15.2-Q11.3.png)
![ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.4](https://www.learninsta.com/wp-content/uploads/2018/08/ML-Aggarwal-Class-10-Solutions-for-ICSE-Maths-Chapter-15-Circles-Ex-15.2-Q11.4.png)
![ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.2 Q11.5](https://www.learninsta.com/wp-content/uploads/2018/08/ML-Aggarwal-Class-10-Solutions-for-ICSE-Maths-Chapter-15-Circles-Ex-15.2-Q11.5.png)
(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