Circles Test - ...

In the given figure, $$AB$$ is a diameter of a circle with centre $$O$$. If $$ADE$$ and $$CBE$$ are straight lines, meeting a $$E$$ such that $$\angle BAD = 35^{o}$$ and $$\angle BED = 25^{o}$$,  Then : (i) $$\angle DCB$$ (ii) $$\angle DBC$$ (iii) $$\angle BDC$$, are respectively.

In the given figure, O is the centre of the circle. If $$\angle AOD = 140^{o}$$ and $$\angle CAB = 50^{o}$$,  then:

$$A, B$$, and $$C$$ are three points on a circle with centre $$O$$ such that $$BOC = 30^o$$ and $$\angle AOB = 60^o$$. If $$D$$ is a point on the circle other than the arc $$ABC$$, find $$\angle ADC$$. 

In the given figure, the two circles intersect at $$P$$ and $$Q$$. If $$\angle A = 80^{o}$$ and $$\angle D = 84^{o}$$, So (i) $$\angle QBC$$, (ii) $$\angle BCP$$ are:

$$AOD$$ is a diameter of the circle with centre $$O.$$ Given that $$\angle BDA=18^{\circ}$$ and $$\angle BDC=38^{\circ}. $$ Find $$\angle BCD$$.

In the given figure $$AB$$ is diameter of circle with centre $$O$$ and chord $$ED$$ is parallel to $$AB$$ and $$\angle EAB=65^o$$. Then $$m\angle EBD$$ is:

Which of the following statement is false?

$$PQRS$$ is a cyclic quadrilateral. Find the measure of $$\angle P$$ and $$\angle Q$$.

The perpendicular drawn from centre to the chord divides the chord in a ratio of _____

$$\text{ABCD}$$ is a cyclic quadrilateral whose side $$\text{AB}$$ is a diameter of the circle through $$\text{A, B, C}$$ and $$\text{D}$$. If $$\angle \text{ADC}=130^{\circ}$$, find $$\angle \text{BAC}$$.