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CBSE Class 10 Triangles and Circles — practice questions — page 2

Explore 50 free Triangles and Circles questions in CBSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Triangles and Circles questions and exercises with answers

Showing questions 31–50 of 50.

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 →Match each circle line to what it doesRead the answer and worked solution →True or false: tangentsRead the answer and worked solution →Key in the tangent answerRead the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →True or false: similar figuresRead the answer and worked solution →Tap what similarity of polygons needsRead the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →Match each geometric similarity theorem with its conclusion:Read the answer and worked solution →

Worked practice questions

A chord of a circle of radius 10 cm subtends a right angle at the centre. The length of the chord is

  1. 10 cm
  2. 5 (square root of 2) cm
  3. 20 cm
  4. 10 (square root of 2) cm
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Correct answer: D. 10 (square root of 2) cm

1. Chord with central angle 90 degrees forms an isosceles right triangle with two radii as legs. 2. Chord squared = 10 squared + 10 squared = 200. 3. Chord = 10 (square root of 2) cm. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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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 is

  1. 7 (square root of 3) cm
  2. 7 cm
  3. 14 cm
  4. 7/2 cm
Show answer and solution

Correct answer: A. 7 (square root of 3) cm

1. Tangent-chord angle 60 means central angle 2 × 60 = 120 degrees subtended by chord. 2. Chord squared = 2 r squared (1 - cos(120)) = 2 × 49 × 3/2 = 147. 3. Chord = square root of 147 = 7 (square root of 3) cm. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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A circle is inscribed in a right triangle whose legs are 5 cm and 12 cm. The radius of the inscribed circle is

  1. 1 cm
  2. 2 cm
  3. 3 cm
  4. 4 cm
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Correct answer: B. 2 cm

1. Hypotenuse = square root of (25 + 144) = 13 cm. 2. For a right triangle, r = (a + b - c)/2 = (5 + 12 - 13)/2. 3. r = 4/2 = 2 cm. _Source: syllabus Mathematics, Ch 10 "Circles", §10.3_

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