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Mathematics

Every cyclic parallelogram is a/an :

  1. square

  2. rhombus

  3. rectangle

  4. isosceles trapezium

Circles

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Answer

Every cyclic parallelogram is a/an : Loci, RSA Mathematics Solutions ICSE Class 10.

Given,

ABCD is a cyclic parallelogram.

∠ABC = ∠ADC [Opposite angles of parallelogram are equal]

∠ABC + ∠ADC = 180° [Sum of opposite angles of cyclic quadrilateral is 180°]

∠ABC + ∠ABC = 180°

2∠ABC = 180°

∠ABC = 1802\dfrac{180^{\circ}}{2}

∠ABC = ∠ADC = 90°

A parallelogram one of whose angle is 90° is a rectangle.

Hence, Every cyclic parallelogram is a rectangle.

Hence, option 3 is the correct option.

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