Circles Test - ...

In a circle of radius $$13 ~cm, PQ$$ and $$RS$$ are two parallel chords of lengths $$24 ~cm$$ and $$10~ cm$$ respectively. Calculate the distance between the chords if they are $$(i)$$ on the same side of the center and $$(ii)$$ on the opposite sides of the center.

In Fig. 2 , the measure of $$\angle B C D$$ is:

In a circle of radius $$2018$$ having center at $$O$$, $$OPQR$$ is a rectangle with $$Q$$ on the circumference of the circle. $$P,R$$ points inside the circle such that $$PQ=504$$. Then $$PR=$$

A,B,C and D be the angles of cyclic quadrilateral taken order , then $$cos({ 180 }^{ \circ  }+A)$$ + $$cos({ 180 }^{ \circ  }+B)$$+$$cos({ 180 }^{ \circ  }+C)$$+$$cos({ 180 }^{ \circ  }+D)$$is equal to 

A square is inscribed in the circle $${ x }^{ 2 }+{ y }^{ 2 }-6x+8y-103=0$$ with its sides parallel to the coordinate axes . Then the distance of the vertex of this square which is nearest to the origin is :

The value of x and y in tyhe fighure are measure of angles,then x+y is equal to 

$$ AB C D$$ is cyclic quadrilateral such that $$AB$$ is a diameter of the circle circumscribing it and $$\angle ADC=130^{ { \circ  } },$$ then the value of $$\angle A B C$$ is:

What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

$$\Box ABCD$$ is a cyclic quadrilateral, $$\angle BAD={ 75 }^{ \circ  },m\angle ADC={ 85 }^{ \circ  }$$. The bisectors of $$\angle ABC$$ and $$\angle BCD$$ meet in the point O. Find m$$\angle BOC.$$

Consider a circle with center O and radius = 20cm. Find the perpendicular distance of a chord of length 32cm from the center of the circle.