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 140० , 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 = 50o, 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