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CBSE Class 10 Triangles and Circles — practice questions

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 1–30 of 50.

In triangle PQR, S and T are points on PQ and PR respectively. ST is parallel to QR. If PS = 3, SQ = 6 and PT = 4, then PR equalsRead the answer and worked solution →A 5 m long ladder leans against a wall with its foot 3 m from the wall. The height it reaches up the wall isRead the answer and worked solution →In two similar triangles the ratio of medians is 3 : 5. The ratio of corresponding sides isRead the answer and worked solution →D, E, F are midpoints of sides BC, CA, AB of triangle ABC. The ratio of areas of triangle DEF and triangle ABC isRead the answer and worked solution →In an isosceles triangle ABC with AB = AC = 13 cm and BC = 10 cm, the altitude from A to BC isRead the answer and worked solution →Two similar triangles have areas 81 sq cm and 144 sq cm. The ratio of their corresponding altitudes isRead the answer and worked solution →In triangle ABC, AD is perpendicular to BC. Given AB = 7 cm, AC = 25 cm, BD = 5 cm, the value of CD isRead the answer and worked solution →The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 60 cm. The area of the triangle isRead the answer and worked solution →ABC is an equilateral triangle of side 2a. The length of its altitude isRead the answer and worked solution →In a quadrilateral ABCD where AB is parallel to CD and the diagonals AC and BD intersect at O, the ratio AO : OC equalsRead the answer and worked solution →Triangles ABC and DEF are similar with AB = 4 cm, BC = 5 cm, CA = 6 cm and EF = 7.5 cm. The perimeter of triangle DEF isRead the answer and worked solution →In triangle ABC, AB squared + BC squared = AC squared and AB = BC. The angles of the triangle areRead the answer and worked solution →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 →

Worked practice questions

In triangle PQR, S and T are points on PQ and PR respectively. ST is parallel to QR. If PS = 3, SQ = 6 and PT = 4, then PR equals

  1. 8
  2. 10
  3. 14
  4. 12
Show answer and solution

Correct answer: D. 12

1. By BPT, PS/SQ = PT/TR. So 3/6 = 4/TR, giving TR = 8. 2. PR = PT + TR = 4 + 8. 3. Hence PR = 12. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.3_

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A 5 m long ladder leans against a wall with its foot 3 m from the wall. The height it reaches up the wall is

  1. 4 m
  2. 3 m
  3. 2 m
  4. 5 m
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Correct answer: A. 4 m

1. Ladder forms hypotenuse 5; wall-foot distance is 3. 2. Height squared = 5 squared minus 3 squared = 25 minus 9 = 16. 3. Hence height = 4 m. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.5_

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In two similar triangles the ratio of medians is 3 : 5. The ratio of corresponding sides is

  1. 9 : 25
  2. 5 : 3
  3. 3 : 5
  4. 3 : 25
Show answer and solution

Correct answer: C. 3 : 5

1. In similar triangles, all linear elements share the same ratio. 2. Medians are linear, so their ratio equals the side ratio. 3. Hence 3 : 5. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.4_

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