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Bihar Board Class 10 (BSEB) Circles — practice questions

Explore 34 free Circles questions in Bihar Board Class 10 (BSEB) 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 1–30 of 34.

A line that intersects a circle at exactly one point is called aRead the answer and worked solution →The tangent at any point of a circle isRead the answer and worked solution →From a point outside a circle, how many tangents can be drawn to the circleRead the answer and worked solution →The lengths of two tangents drawn from an external point to a circle areRead the answer and worked solution →A tangent PT is drawn from a point P to a circle with centre O. The triangle OPT formed by joining OT isRead the answer and worked solution →The maximum number of common tangents that can be drawn to two non-intersecting circles isRead the answer and worked solution →A point P is 17 cm from the centre of a circle of radius 8 cm. The length of the tangent from P to the circle isRead the answer and worked solution →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

A line that intersects a circle at exactly one point is called a

  1. Tangent
  2. Chord
  3. Secant
  4. Diameter
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Correct answer: A. Tangent

1. A secant cuts the circle at two points; a chord lies inside. 2. A tangent touches the circle at exactly one point. 3. Hence the answer is tangent. _Source: syllabus Mathematics, Ch 10 "Circles", §10.1_

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The tangent at any point of a circle is

  1. Parallel to the radius at the point of contact
  2. Perpendicular to the radius at the point of contact
  3. At 45 degrees to the radius
  4. Coincident with the radius
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Correct answer: B. Perpendicular to the radius at the point of contact

1. Tangent-radius theorem: the tangent at a point on a circle is perpendicular to the radius drawn to that point. 2. Angle between tangent and radius is 90 degrees. 3. Hence option B. _Source: syllabus Mathematics, Ch 10 "Circles", §10.2_

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From a point outside a circle, how many tangents can be drawn to the circle

  1. One
  2. Three
  3. Two
  4. Four
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Correct answer: C. Two

1. From an external point exactly two tangents can be drawn to a circle. 2. From a point on the circle, exactly one tangent; from inside, none. 3. Hence two. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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