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Circles

True Or False

11. Sector is the region between the chord and its corresponding arc.

False

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12. A circle is a plane figure.

True

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Short Answer Type

13. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

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14. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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Long Answer Type

15.

AC and BD are chords of a circle which bisect each other. Prove that:
(i) AC and BD are diameters.
(ii) ABCD is a rectangle.

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Short Answer Type

16. Prove that equal chords of a circle subtend equal angles at the centre.

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17. In the figure, AOC is a diameter of the circle and

arcAXB equals 1 half arcBYC. space Find space angle BOC.

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18. In the adjoining figure is a circle with centre O. If ∠BAC = 60° and ∠DCB = 100°, then find ∠DBC.

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19. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

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20. Suppose you are given a circle. Give a construction to find its centre.

Steps of Construction:
(i) Take any three points P, Q and R on the circle.
(ii) Join PQ and QR.
(iii) Draw the perpendicular bisectors of PQ and QR. Let these intersect at O.
Then, O is the centre of the circle.

Steps of Construction:(i) Take any three points P, Q and R on the cir

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