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If a pair of opposite angles of a quadrilateral is complementary, then the quadrilateral is cyclic quadrilateral

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Important Questions on Circle

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In the figure, points P,Q,R and S lie on a circle. Then the values of x and y are respectively

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HARD
The points A, B, C, D, E  are marked on the circumference of a circle in clockwise direction such that ABC=130o and CDE=110o. The measure of ACE in degree is
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If all the four vertices of a quadrilateral ABCD lie on the circle and mD=60° then mB= _____.
MEDIUM
It is known that area of a cyclic quadrilateral is (s-a)(s-b)(s-c)(s-d) where a,b,c,d are the sides and s=a+b+c+d2. If a circle can also be inscribed in the cyclic quadrilateral then the area of this quadrilateral is
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In figure PQ, is a chord of a circle with centre O and PT is its tangent at P. if QPT=60°, then PRQ is

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EASY

The sum of pairs of opposite angles of a cyclic quadrilateral is

MEDIUM
Let ABCD be a quadrilateral such that there exists a point E inside the quadrilateral satisfying AE=BE=CE=DE. Suppose DAB, ABC, BCD is an arithmetic progression. Then the median of the set DAB,ABC,BCD is :-
MEDIUM

In the figure PQRS is cyclic side PQ side RQ.PSR=110° find m(arcQR)

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MEDIUM

In the figure PQRS is cyclic. Side PQSide RQ.PSR=110° find m(arc PQR)

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MEDIUM

In the given figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively.

IfCBF=130° and CDE=x° find the value of x

 

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HARD
ABCD is cyclic quadrilateral. AB is the diameter of the circle through points A, B, C and D. If BAC = 35°,  the  ADC is equal to


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HARD

In the given figure, AB is a diameter of a circle with center O and DOCBIf BCD=120° calculate ADC

  Also, show that AOD is an equilateral triangle.

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HARD

In a cyclic quadrilateral ABCD, if B-D=60°, show that the smaller of the two is 60°.

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In the given figure, ABC is an isosceles triangle in which  AB=AC and a circle passing through B and C intersects AB and AC at D and E respectively.

Prove that DEBC.

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HARD

AC and BD are chords of a circle which bisect each other. Prove that ABCD is a rectangle.

HARD
In ABC, AD and BE are altitudes. Prove that, ar (DEC)ar (ABC)=DC2AC2
HARD
ABCD is cyclic quadrilateral inscribed in a circle with the centre O. Then OAD is equal to




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EASY

Is the picture given a tessellation?

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