# In Fig. 10.6, if OAB = 40 �, then ACB is equal to: A. 50 �B. 40 �C. 60 �D. 70°

In triangle AOB,

OAB = OBA = 40° ( angles opposite to equal sides are equal)

Using the angle sum property of triangle, sum of all angles of a triangle is 180°,

OAB + OBA + AOB = 180°

40° + 40° + AOB = 180°

AOB = 180° - 40° - 40°

AOB = 100°

By theorem “The angle subtended by an arc at the center of a circle is twice the angle subtended by it at remaining part of the circle”, we have:

AOB = 2 × ACB

ACB = AOB/2

= 100°/2

ACB = 50°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  RD Sharma | Extra Qs. of Cyclic Quadrilaterals31 mins  Important Questions on Circles29 mins  NCERT | Imp. Qs. on Circles43 mins  Quiz | Lets Roll on a Circle45 mins  Proof of Important Theorems of Circles45 mins  Concept of Cyclic Quadrilateral61 mins  Master Theorems in Circles42 mins  Proof of Important Theorems of Circles46 mins  Genius Quiz | Rolling Around Circles49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 