Q. 8

# In the picture below, ABCD is a square with vertices on a circle and XYZ is such an equilateral triangle. P and Q are points on the circules: i) How much is □ APB?ii) How much is □ XQZ?

(i)  Join AC.

Now, APBC is a cyclic quadrilateral, as it lies on a circle

Therefore,

APB + ACB = 180° [Sum of opposite angles of a cyclic quadrilateral is 180°]

Now, Diagonals of the square bisects the angles of a square  APB + 45° = 180°

APB = 135°

(ii) As, XYZQ is a cyclic quadrilateral

XYZ + XQZ = 180° [Sum of opposite angles of a cyclic quadrilateral is 180°]

Now, XYZ = 60°, as XYZ is an equilateral triangle

XQZ = 180° – 60° = 120°

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz | Imp. Qs. on Circle35 mins  Quiz | Imp. Qs. on Circles37 mins  Quiz | Testing Your Knowledge on Circles32 mins  Short Cut Trick to Find Area of Triangle43 mins  Quiz | Areas Related to Circles43 mins  RD Sharma | Area of Sector and Segments25 mins  Quiz | Area Related with Circles47 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 