Skip to content 1 ABCD is a cyclic quadrilateral inscribed in a circle.
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2 Quadrilateral PQRS is inscribed in a circle.
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3 Consider a cyclic quadrilateral.
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4 The distance of a chord of length 16 cm from the centre of a circle is 6 cm.
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5 A cyclic quadrilateral has sides 5, 5, 12, 12 units.
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6 When two chords intersect, each of them is divided into two-line segments.
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7 Draw a circle in which a chord of 6 cm length stands at a distance of 3 cm from the centre.(Hint: Is it a circumcircle of a suitable triangle?)
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8 Show that rectangle is the only parallelogram that can be inscribed in a circle.
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9 Consider all chords of a circle of a fixed length.
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10 In a circle with centre O, chords AB and AC are congruent.
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11 Show that if a rectangle is inscribed in a circle, then the point of intersection of its diagonals must lie at the centre of the circle.
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12 Two parallel chords of lengths 10 cm and 24 cm are on the same side of the centre of a circle.
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13 A quadrilateral MNOP is inscribed in a circle.
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14 'There is no chord of a circle that is longer than its diameter.' How do you justify this statement?
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15 A regular hexagon is inscribed in a circle of radius r.
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16 Let ABCD be a cyclic quadrilateral.
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17 Let A be any point within a given circle with centre O.
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18 In a circle, two chords CC' and DD' are drawn perpendicular to a diameter AB.
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19 How would you use given figure to justify the statement that the sum of the opposite angles of a cyclic quadrilateral is 180^?
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20 How would you use given figure to justify the statement that the angle in a semicircle is 90^?
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21 Explain why the following statement is true: If the perpendicular distance of a chord from the centre is d and the radius is r, then the chord length is 2sqrt((r2 - d2)).
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22 In a circle, if the distance of chord AB from the centre is twice the distance of another chord CD from the centre, then can we conclude that CD = 2AB?
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23 Jamuna has a circular piece of paper.
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24 Let A and B be two points on a circle with centre O.
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25 Find x in the given figure.
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26 In a circle with centre O, the central angle AOB = 60^.
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27 What are the rotational symmetries of a square?
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28 What is the length of the longest chord in a circle of radius 5 units?
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29 The locus of points at a given distance from a given point is a circle.
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30 Are there circles of all possible radii passing through A and B?
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