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NCERT Solutions for Class 9 Maths Chapter 10 Circles

Write True or False: Give reasons for your answers. All the line segment from the centre to the circle is of equal length. We can draw infinite numbers of equal chords.

We get cy and minor arcs for unequal arcs. A chord which is twice as long as radius must pass through the centre of the circle and is diameter to the circle.

Sector is the region between the arc and the two radii of the circle. A circle can be drawn on the plane. 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. A circle is a collection of points whose every every point is equidistant from the centre.

Thus, two circles can only be congruent when they the distance of every point of the both circle is equal from the centre. Equal chords of congruent circles subtend clads angles at their centres.

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

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? Steps of construction: Step I: A circle is drawn.

Step IV: Let these two perpendicular bisector meet at a point. The point of intersection of these two perpendicular bisector class 9 maths ch 10 ex 10.2 visa the centre of the circle. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

Given, Two circles which intersect each other at P and Q. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord. If two equal chords of a circle clqss within the circle, prove that the segments cllass one chord are equal to corresponding segments of the other chord.

OE is joined. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes class 9 maths ch 10 ex 10.2 visa angles with the chords.

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a 10.2. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip? BM is perpendicular clas of AC and thus it passes through the centre of the circle. A circular park of radius 20m is situated in a colony.

Three boys Ankur, Syed and David are sitting at equal distance on its boundary each class 9 maths ch 10 ex 10.2 visa a toy telephone in his hands to talk each. Find the length of the string of each phone. All three boys at equal distances thus ABC is an equilateral triangle. OA is the radius of the triangle.

In Fig. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at class 9 maths ch 10 ex 10.2 visa point on the major arc.

Answer Given, AB is equal to the radius of the circle. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. To prove, ABCD is cyclic trapezium. Two circles intersect at two points B and C.

Chords AP and DQ are joined. If circles are drawn cllass two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third. The circles intersected at D. Thus, D lies on the BC.

Given, AC is the common hypotenuse. These angles are in the semi circle. Thus, both the triangles are lying in the semi circle and AC is the diameter of the circle. Thus, CD is the chord. Thus, ABCD is a rectangle.

What are the components of a circle? Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Two chords AB and CD of lengths 5 cm and 11 cm, respectively of a circle are parallel to each other and are on opposite sides of its centre. If the angles subtended by two chords of a circle at the centre are equal, the chords are also equal. Hence, points A, B, C and D lie on the same circle.

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