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Porperty of cyclic quadrilateral

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Porperty of cyclic quadrilateral

    • Posted by ? ☺ 6 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 6 years, 3 months ago

    Cyclic Quadrilateral Properties

    • In a cyclic quadrilateral, the sum of a pair of opposite angles is 1800. (supplementary).
    • If the sum of two opposite angles are supplementary then it’s a cyclic quadrilateral.
    • The area of a cyclic quadrilateral is [s(s-a)(s-b)(s-c)(s-c)]0.5 where a, b, c, and d are the four sides of the quadrilateral and the perimeter is 2s.
    • The four vertices of a cyclic quadrilateral lie on the circumference of the circle.
    • To get a rectangle or a parallelogram, just join the midpoints of the four sides in order.
    • If PQRS is a cyclic quadrilateral, then ∠SAR = ∠SQR, ∠QPR = ∠QSR, ∠PQS = ∠PRS, ∠QRP = ∠QSP.
    • If T is the point of intersection of the two diagonals, PT X TR = QT X TS
    • The exterior angle formed if any one side of the cyclic quadrilateral is produced is equal to the interior angle opposite to it.
    • In a given cyclic quadrilateral, d1 / d2  = sum of the product of sides, which shares the diagonals endpoints.
    • If it is cyclic quadrilateral then the perpendicular bisectors will be concurrent compulsorily.

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