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PQRS is a cyclic quadrilateral and RS is a diameter. If SPQ =  140 o RSQ is equal to


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Important Questions on Circles

EASY

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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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
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 :-
EASY

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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EASY

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

EASY
If all the four vertices of a quadrilateral ABCD lie on the circle and mD=60° then mB= _____.
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
MEDIUM
Prove that, any rectangle is a cyclic quadrilateral.
EASY
A parallelogram is always a trapezium.
MEDIUM
Prove that the diagonals of a rectangle inscribed in a circle are the diameters of the circle. 
EASY
MRPN is cyclic, R=(5x-13)°,N=(4x+4)°. Find measures of R and N
MEDIUM
In a cyclic quadrilateral ABCD, twice the measure of A is thrice the measure of C. Then, the measure of C is
EASY

Write the quadrants in which the following points lie:

-4,7

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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MEDIUM
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a
EASY
Which one has all the properties of a kite and a parallelogram?
EASY
All squares are rhombuses and also rectangles.