The product of the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the product of its two pairs of opposite sides. The perpendicular bisectors of the fours sides of the inscribed quadrilateral intersect at the center O.
the sum of the opposite angles is equal to 180˚. Consider the diagram below. If a, b, c and d are the internal angles of the inscribed quadrilateral, then. a + b = 180˚ and c + d = 180˚.
Opposite angles of a cyclic quadrilateral are supplementary.
Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
Let, the exterior angle, angle CDE = x.
and, it's opposite interior angle is angle ABC.
as, ADE is a straight line.
so, angle ADC = (180-x) degrees.
since, opposite angles of a cyclic quadrilateral are supplementary,
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Answer:
The product of the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the product of its two pairs of opposite sides. The perpendicular bisectors of the fours sides of the inscribed quadrilateral intersect at the center O.
the sum of the opposite angles is equal to 180˚. Consider the diagram below. If a, b, c and d are the internal angles of the inscribed quadrilateral, then. a + b = 180˚ and c + d = 180˚.
Opposite angles of a cyclic quadrilateral are supplementary.
Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
Let, the exterior angle, angle CDE = x.
and, it's opposite interior angle is angle ABC.
as, ADE is a straight line.
so, angle ADC = (180-x) degrees.
since, opposite angles of a cyclic quadrilateral are supplementary,
angle ABC = x.