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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

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
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

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

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 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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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
If all the four vertices of a quadrilateral ABCD lie on the circle and mD=60° then mB= _____.
MEDIUM
If P, Q, S and R are points on the circumference of the circle of radius r, such that PQR is an equilateral triangle and PS is the diameter of the circle. Then, the perimeter of the quadrilateral PQSR will be
HARD
ABCD is cyclic quadrilateral inscribed in a circle with the centre O. Then OAD is equal to




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MEDIUM

In the given figure, if the chord ED is parallel to the diameter AC. Then, the measure of CED will be

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EASY
The opposite angles in a cyclic quadrilateral add up to _____ degree.
EASY

In the following figures A, B, C and D (if marked in the figure) lie on the circle. Point O (if marked in the figure) is the centre of the circle.

Which of the following figures has a cyclic quadrilateral?

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In the diagram given below ABCD is a cyclic quadrilateral. The value of BCE=_____°

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MEDIUM
If one side of a cyclic quadrilateral is produced then the exterior angle is _____ to the interior opposite angle.
EASY
If a pair of opposite angles of a quadrilateral are supplementary, then the quadrilateral is a _____ quadrilateral
HARD
PQRS is a cyclic quadrilateral and RS is a diameter. If SPQ =  140 o RSQ is equal to


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HARD

In figure, AOB  is the diameter of a circle and C,D and E are three points situated on semi circle. The value of ACD+BED=_____°

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MEDIUM
In a cyclic quadrilateral ABCD, twice the measure of A is thrice the measure of C. Then, the measure of C is
MEDIUM

In the given figure, if POR=110°, then the value of PQR is 

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