MEDIUM
9th Kerala Board
IMPORTANT
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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.

Important Questions on Circles

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.
MEDIUM
9th Kerala Board
IMPORTANT
Standard 9 Mathematics Part - 1>Chapter 5 - Circles>Exercise 4>Q (3)
Find the relation between the length of a side and the circumradius of an equilateral triangle.