Circles Test - ...

In the given figure, $$\triangle XYZ$$ is inscribed in a circle with centre $$O$$. If the length of chord $$YZ$$ is equal to the radius of the circle $$OY$$, then $$\angle YXZ$$ is equal to 

In the given figure, $$ABCD$$ is a cyclic quadrilateral in which $$\angle CAD = 25^{o}, \angle ABC = 50^{o}$$ and $$\angle ACB = 35^{o}$$.

Two circle intersect at $$A$$ and $$B$$. Quadrilaterals $$PCBA$$ and $$ABDE$$ are inscribed in these circles such that $$PAE$$ and $$CBD$$ are line segments. Also, $$\angle$$P = 95$$^o$$ and $$\angle$$C = 40$$^o$$. The value of $$Z$$ is:

In the given figure, $$PQRS$$ is a cyclic trapezium in which $$PQ\parallel SR$$. If $$\angle$$P = 82$$^o$$, then $$\angle$$S is:

In the figure, $$AB$$ is parallel to $$DC$$, $$\angle BCD=80^o$$ and $$\angle BAC = 25^o$$. Then $$\angle CAD$$ is:

In the given figure, $$I$$ is the incentre of $$\Delta ABC$$. $$AI$$ produced meets the circumcircle of $$\Delta ABC$$ at $$D$$; $$\angle ABC = 55^{o}$$ and $$\angle ACB = 65^{o}$$.  Then  (i) $$\angle BCD$$ (ii) $$\angle CBD$$ (iii) $$\angle DCI$$ (iv) $$\angle BIC$$ are respectively:

In the given figure, $$AB$$ is a diameter of a circle with the centre $$O$$ and chord $$ED$$ is parallel to $$AB$$ and $$\angle EAB = 65^{o}$$.  (i) $$\angle EBA$$ (ii) $$\angle BED$$ (iii) $$\angle BCD$$ are respectively:

In the adjoining figure, two circles intersect at $$A$$ and $$B$$. The centre of the smaller circle is $$O$$ and lies on the circumference of the larger circle. If $$PAC$$ and $$PBD$$ are straight lines and $$\angle APB = 75^{o}$$, find (i) $$\angle AOB$$, (ii) $$\angle ACB$$, (ii) $$\angle ADB$$. 

Two circles intersect in $$A$$ and $$B$$. Quadrilaterals $$PCBA$$ and $$ABDE$$ are inscribed in these circles such that $$PAE$$ and $$CBD$$ are line segments. If $$\angle P=95^o$$ and $$\angle C=40^o$$. Also, $$ \angle AED=z. $$ Then the value of $$z$$ is:

$$ABCD$$ is a cyclic quadrilateral whose diagonals intersect at a point $$E$$. If $$\angle DBC = 70^o, \angle BAC = 30^o$$, find $$\angle BCD$$. Further, if AB= BC, find $$\angle ECD$$.