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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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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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
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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.
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