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Andhra Pradesh SSC (Class 10) Triangles and Circles — practice questions — page 2

Explore 50 free Triangles and 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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Triangles and Circles questions and exercises with answers

Showing questions 31–50 of 50.

In two similar triangles the ratio of medians is 3 : 5. The ratio of corresponding sides isRead the answer and worked solution →In triangle ABC right-angled at B, BD is perpendicular to AC. If AB = 5 cm and BC = 12 cm, then BD equalsRead 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 a right triangle with legs a and b, the altitude h drawn to the hypotenuse c satisfiesRead the answer and worked solution →In triangle ABC, points P and Q are on AB and AC such that PQ is parallel to BC. If AP = x, PB = 6, AQ = 4, QC = 9, then x equalsRead 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 →

Worked practice questions

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
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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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In triangle ABC right-angled at B, BD is perpendicular to AC. If AB = 5 cm and BC = 12 cm, then BD equals

  1. 12/5 cm
  2. 13/12 cm
  3. 5/12 cm
  4. 60/13 cm
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Correct answer: D. 60/13 cm

1. Area of triangle ABC = 1/2 × AB × BC = 1/2 × 5 × 12 = 30 sq cm. 2. AC by Pythagoras = square root of (25 + 144) = 13 cm. 3. Area also equals 1/2 × AC × BD = 1/2 × 13 × BD. So BD = 60/13 cm. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.5_

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D, E, F are midpoints of sides BC, CA, AB of triangle ABC. The ratio of areas of triangle DEF and triangle ABC is

  1. 1 : 4
  2. 1 : 3
  3. 1 : 2
  4. 1 : 6
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Correct answer: A. 1 : 4

1. Joining midpoints creates a medial triangle DEF similar to ABC. 2. Each side of DEF is half the parallel side of ABC, so side ratio is 1 : 2. 3. Area ratio is the square: 1 : 4. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.4_

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More Mathematics topics

Real Numbers and PolynomialsArithmetic ProgressionStatistics and ProbabilityQuadratic EquationsLinear Equations in Two VariablesIntroduction to TrigonometrySurface Areas and VolumesAreas Related to Circles