Circles Test - ...

If A, B, C, D are four points such that $$ \angle BAC={ 30 }^{ \circ } $$ & $$\angle BDC={ 60 }^{ \circ },$$ then D is the center of the circle through A, B and C. The statement is

In figure if  $$\angle AOB={ 90 }^{ o }\ and\ \angle ABC={ 30 }^{ o }$$ then angle CAO is equal to 

$$AD$$ is a diameter of a circle and $$AB$$ is a chord. If $$AD = 34\> cm, AB = 30\ cm$$, the distance of $$AB$$ from the centre of the circle is

If $$AB = 12$$ cm, $$BC = 16$$ cm and $$AB$$ is perpendicular to $$BC$$, then the radius of the circle passing through the points $$A$$, $$B$$ and $$C$$ is:

The angles of a cyclic quadrilateral $$ABCD$$ are $$A = (6x + 10) $$, $$B = (5x)$$, $$C = (x + y)$$, $$D = (3y -10)$$.
Find $$x$$ and $$y$$, and hence find the values of the four angles.

In given figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of $$ \angle ACD+\angle BED. $$

If the sum of the circumferences of two circles with radii $$R_1$$ and $$ R_2$$ is equal to the circumference of a circle of radius $$R$$, then

Area of the largest triangle that can be inscribed in a semi-circle of radius $$r$$ units is

A quadrilateral $$ABCD$$ is inscribed in a circle such that $$AB$$ is a diameter and $$ \angle ADC={ 130 }^{ o }$$, then $$m\angle BAC= $$?