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Andhra Pradesh SSC (Class 10) Circles — practice questions

Explore 23 free Circles questions in Andhra Pradesh SSC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Circles questions and exercises with answers

Showing questions 1–23 of 23.

Two concentric circles have radii 5 cm and 13 cm. The length of a chord of the larger circle that touches the smaller circle isRead the answer and worked solution →The radius of a circle is 6 cm. The length of the tangent from a point 10 cm from the centre isRead the answer and worked solution →A circle has centre O. A tangent at P makes an angle of 30 degrees with chord PQ. Then angle POQ equalsRead the answer and worked solution →In a quadrilateral ABCD circumscribed about a circle, AB + CD equalsRead the answer and worked solution →Two tangents PA and PB are drawn from an external point P to a circle. If angle APB = 60 degrees, then angle AOB equalsRead the answer and worked solution →The length of a tangent from a point at distance c from the centre of a circle of radius r isRead the answer and worked solution →Two circles of radii 5 cm and 3 cm touch each other internally. The distance between their centres isRead the answer and worked solution →Two circles of radii 5 cm and 3 cm touch each other externally. The distance between their centres isRead the answer and worked solution →A tangent at point A of a circle of radius 5 cm meets a line through the centre at B such that AB = 12 cm. The length of OB isRead the answer and worked solution →PA and PB are tangents from external point P to a circle with centre O. If PA = 12 cm and the radius is 5 cm, then OP equalsRead the answer and worked solution →The maximum number of common tangents to two circles that intersect at two points isRead the answer and worked solution →A chord of a circle of radius 10 cm subtends a right angle at the centre. The length of the chord isRead the answer and worked solution →In a circle of radius 7 cm, a tangent and a chord meet at the point of contact with an angle of 60 degrees. The length of the chord isRead the answer and worked solution →A circle is inscribed in a right triangle whose legs are 5 cm and 12 cm. The radius of the inscribed circle isRead the answer and worked solution →Two tangents from an external point to a circle of radius 6 cm have length 8 cm each. The distance of the external point from the centre isRead the answer and worked solution →A line drawn through the centre of a circle to bisect a chord isRead the answer and worked solution →PA and PB are tangents from a point P to a circle. If angle APB = 90 degrees, the radius and PA are related byRead the answer and worked solution →A circle touches all four sides of a quadrilateral ABCD with AB = 6, BC = 7, CD = 4. Then AD equalsRead the answer and worked solution →A tangent at point P of a circle of radius 5 cm is parallel to a chord 8 cm long. The distance of the chord from the centre isRead the answer and worked solution →Two parallel tangents are drawn to a circle of radius 8 cm. The distance between them isRead the answer and worked solution →A point P is 25 cm away from the centre O of a circle and the tangent PT to the circle is 24 cm long. The radius of the circle isRead the answer and worked solution →In a circle, two chords AB and CD intersect inside at P. If AP × PB = 8 and CP = 4, then PD equalsRead the answer and worked solution →Two circles touch each other externally at P. A common tangent at P meets another common tangent AB at point M. Then AM equalsRead the answer and worked solution →

Worked practice questions

Two concentric circles have radii 5 cm and 13 cm. The length of a chord of the larger circle that touches the smaller circle is

  1. 12 cm
  2. 13 cm
  3. 18 cm
  4. 24 cm
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Correct answer: D. 24 cm

1. The chord is a tangent to the smaller circle; perpendicular from centre = 5 cm. 2. Half-chord squared = 13 squared minus 5 squared = 169 minus 25 = 144. 3. Half-chord = 12; full chord = 24 cm. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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The radius of a circle is 6 cm. The length of the tangent from a point 10 cm from the centre is

  1. 8 cm
  2. 10 cm
  3. 6 cm
  4. 4 cm
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Correct answer: A. 8 cm

1. Tangent length squared = 10 squared minus 6 squared = 100 minus 36 = 64. 2. Tangent length = 8 cm. 3. Hence option A. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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A circle has centre O. A tangent at P makes an angle of 30 degrees with chord PQ. Then angle POQ equals

  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 120 degrees
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Correct answer: B. 60 degrees

1. Tangent-chord angle equals the inscribed angle in the alternate segment. 2. Inscribed angle subtending PQ is 30 degrees. 3. Central angle POQ = 2 × inscribed = 60 degrees. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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More Mathematics topics

Real Numbers and PolynomialsArithmetic ProgressionStatistics and ProbabilityQuadratic EquationsLinear Equations in Two VariablesTriangles and CirclesIntroduction to TrigonometrySurface Areas and Volumes