Chapter-10. Circles Mathematics class 9 in english Medium CBSE Notes

Important-Question for Assignment:   

Q1. The bisector of ∠B of an isosceles triangle ABC with AB = Ac meets the circumcircle of  ABC at P as shown in figure. If AP abd BC produced meet at Q, prove that CQ = CA. 

Q2. In the given figure, O is the centre of the circle. The angle substended by arc ABC at the centre is 140^० , AB is produced to P. Determine ∠ADC and ∠CBP.  

Q3. In the given figure, O is the centreand Ae is the semi-circle ABCDE. If AB = BC and ∠AEC = 50^o, then find 

(i) ∠CBE 

(ii) ∠CDE 

(iii) ∠AOB 

​(iv) Prove that BO|| CE 

Q4.  In figure, P is the centre of  the circle. Prove that 

         ∠XPZ = 2 (∠XZY + ∠YXZ) 

Q5. In given fig. B and E are the midpoint on respectively on line segment AC and DF. Show that AD||CF.

Q6. Find the value of x see given figure.

Q7.  ABCD is a parallelogram. The circle through A, B and C intersects CD produced at E, prove that AE = AD. 

Q8. In the given Figure, find the value of x. 

                 ​

Q9. L and M are the mid-point of two equal chords AB and CD and O is the centre of the circle. Prove that 

(i) ∠OLM = ∠OML 

(ii) ∠ALM = ∠CML