In following figure, two congruent circles have centres O and O′. Arc AXB subtends an angle of 75° at the centre O and arc A′ Y B′ subtends an angle of 25° at the centre O′. Then the ratio of arcs A X B and A′ Y B′ is

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In following figure, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150°, then ∠APQ is equal to

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AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is


In following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

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If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:


In following figure, if ∠ABC = 20º, then ∠AOC is equal to:

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In following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to:

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In following figure, if ∠OAB = 40º, then ∠ACB is equal to:

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In following figure, if ∠DAB = 60º, ∠ABD = 50º, then ∠ACB is equal to:

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ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to:


In following figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to:

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Additional Information:

This quiz is based on Exemplar Problems and other important questions from the "Circles" chapter of the Mathematics subject for CBSE NCERT Class 9 (IX). It covers key concepts such as chords, tangents, arcs, cyclic quadrilaterals, and important theorems related to circles. These questions are designed to help students strengthen their understanding and improve problem-solving skills. For more such resources, visit the official NCERT website.