MEDIUM
9th Kerala Board
IMPORTANT
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Prove that chords of the same length in a circle are at the same distance from the centre.

Important Questions on Circles

MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 2>Q (2)
Two chords intersect at a point on a circle and the diameter through this point bisects the angle between the chords. Prove that the chords have the same length.
MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 2>Q (3)
In the picture given below, the angles between the radii and the chords are equal. Prove that the chords are of the same length.
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EASY
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 3>Q (1)
In a circle, a chord 1 cm away from the centre is 6 cm long. If the length of a chord 2 cm away from the centre is 2k cm, then find the value of k.
EASY
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 3>Q (2)
In a circle of radius 5 cm, two parallel chords of lengths 6 cm and 8 cm are drawn on either side of a diameter. What is the distance between them? If parallel chords of these lengths are drawn on the same side of a diameter, what would be the distance between them?
MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 3>Q (3)
The bottom side of the quadrilateral in the picture is a diameter of the circle and the top side is a chord parallel to it. Calculate the area of the quadrilateral in square centimetres.
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MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 3>Q (4)
In a circle, two parallel chords of lengths 4 and 6 centimetres are 5 centimetres apart. If the radius of the circle is k then find the value of k.
MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 4>Q (1)
Draw three triangles with lengths of two sides 4 cm and 5 cm and angle between them 60°, 90° and 120°. Draw the circumcircle of each. (Note how the position of the circumcentre changes).
MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 4>Q (2)
The equal sides of an isosceles triangle are 8 cm long and the radius of its circumcircle is 5 cm. Calculate the length of its third side in centimetres.