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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Ncert Math Solutions Class 9th Chapter 10 Circles Exercise 10.2 Question 2
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Ncert Math Solutions Class 9th Chapter 10 Circles Exercise 10.2 Question 1
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.
Ncert Math Solutions Class 9th Chapter 10 Circles Exercise 10.1 Question 2
Write True or False: Give reasons for your answers.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
True
(ii) A circle has only finite number of equal chords.
This is false because we can have infinite diameters in a circle. Diameter is the longest chord.
(iii) If a circle is divided into three equal arcs, each is a major arc.
False
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
True
(v) Sector is the region between the chord and its corresponding arc.
This is false because segment is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.
True
Ncert Math Solutions Class 9th Chapter 10 Circles Exercise 10.1 Question 1
1. Fill in the blanks:
(i) The centre of a circle lies in interior of the circle. (exterior/ interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in exterior of the circle. (exterior/ interior)
(iii) The longest chord of a circle is a diameter of the circle.
(iv) An arc is a semi-circle when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and the chord of the circle.
(vi) A circle divides the plane, on which it lies, in three parts.
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