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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
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE=AD.
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
If a pair of opposite angles of a quadrilateral are supplementary, then the quadrilateral is a _____ quadrilateral
HARD

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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EASY
If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is 
MEDIUM
In a cyclic quadrilateral ABCD, twice the measure of A is thrice the measure of C. Then, the measure of C is
HARD

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

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

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

EASY

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

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EASY

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

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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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MEDIUM
If one side of a cyclic quadrilateral is produced then the exterior angle is _____ to the interior opposite angle.
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
EASY
Opposite angles of a cyclic quadrilateral are _____.
EASY
If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is _____ quadrilateral
HARD

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