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Mathematics - Properties of Triangles

Practise 43 KVPY previous year questions on Properties of Triangles, compiled from papers spanning 2010 to 2020. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Let A , B , C be three points on a circle of radius 1 such that A C B = 4 . Then the length of the side A B is2020 (SA)
  2. 2In a triangle A B C , a point D is chosen on B C such that B D : D C = 2 : 5 . Let P be a point on the circumcircle A B C such that P D B = 2020 (SA)
  3. 3In a triangle A B C , the altitude A D and the median A E divide A into three equal parts. If B C = 28 , then the nearest integer to A B + A2020 (SA)
  4. 4Let A B C be a triangle such that A B = 4 , B C = 5 and C A = 6 . Choose points D , E , F on A B , B C , C A respectively, such that A D = 22020 (SA)
  5. 5Let A B C be a triangle such that A B = 15 and A C = 9 . The bisector of B A C meets B C in D . If A C B = 2 A B C , then B D is2020 (SB/SX)
  6. 6In a triangle A B C , the angle bisector B D of B intersects A C in D . Suppose B C = 2 , C D = 1 and B D = 3 2 . The perimeter of the trian2020 (SB/SX)
  7. 7Six consecutive sides of an equiangular octagon are 6 , 9 , 8 , 7 , 10 , 5 in that order. The integer nearest to the sum of the remaining tw2020 (SB/SX)
  8. 8Let a = B C , b = C A , c = A B be the side lengths of a triangle A B C , and m be the length of the median through A . If a = 8 , b - c = 22020 (SB/SX)
  9. 9Let A B C be an equilateral triangle with side length a. Let R and r denote the radii of the circumcircle and the incircle of triangle A B C2019 (SA)
  10. 10In a triangle A B C , B A C = 90 ; A D is the altitude from A on to B C . Draw D E perpendicular to A C and D F perpendicular to A B . Suppo2019 (SA)
  11. 11Let l 0 be a real number, C denote a circle with circumference l and T denote a triangle with perimeter l . Then2019 (SA)
  12. 12The sides a , b , c of a triangle satisfy the relations c 2 = 2 a b and a 2 + c 2 = 3 b 2 . Then the measure of B A C , in degrees, is2019 (SA)
  13. 13Let A B C be a triangle in which A B=B C. Let X be a point on A B, such that A X : X B = A B : A X . If A C = A X , then the measure of A B 2019 (SA)
  14. 14The points C and D on a semicircle with A B as diameter are such that A C = 1 , C D = 2 and D B = 3 . Then, the length of A B lies in the in2019 (SB/SX)
  15. 15Let A B C be a triangle and let D be the mid-point of B C . Suppose cot C A D : cot B A D = 2 : 1 . If G is the centroid of A B C , then the2019 (SB/SX)
  16. 16Let a , b , c be the side-length of a triangle and l , m , n be the lengths of its medians. Put K = l + m + n a + b + c Then, as a , b , c v2018 (SA)
  17. 17Consider a P Q R in which the relation Q R 2 + P R 2 = 5 P Q 2 holds. Let G be the point of intersection of medians P M and Q N . Then, Q G 2018 (SA)
  18. 18Let P Q R be an acute-angled triangle in which P Q Q R . From the vertex Q draw the altitude Q Q 1 the angle bisector Q Q 2 and the median Q2018 (SA)
  19. 19Let P Q R be a triangle is which P Q = 3 . From the vertex R , draw the altitude R S to meet P Q at S . Assume that R S = 3 and P S = Q R . 2018 (SA)
  20. 20Let be respectively the areas of a regular pentagon, regular hexagon and regular heptagon which are inscribed in a circle of radius 1 . Then19 Nov, 2017 (SA)
  21. 21Let be a nine-sided regular polygon with side length 2 units. The difference between the lengths of the diagonals and equals05 Nov, 2017 (SA)
  22. 22Three circles of radii 1,2 and 3 units respectively touch each other externally in the plane. The circumradius of the triangle formed by joi2016 (SA)
  23. 23The points are marked on the circumference of a circle in clockwise direction such that and . The measure of in degrees is2016 (SA)
  24. 24Consider a semicircle of radius 1 unit constructed on the diameter , and let be its centre. Let be a point on such that . Draw perpendicular2016 (SA)
  25. 25Suppose we have to cover the xy-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that2016 (SB/SX)
  26. 26Let be a sector of a circle with centre and radius d, , and be a point on such that is perpendicular . Let be the midpoint of and be a point2016 (SB/SX)
  27. 27Let be an interior point of a triangle . Let and be the reflections of in and , respectively. IF are collinear then equals.2015 (SA)
  28. 28Suppose is a hexagon such that and 2. If the vertices are concyclic, the radius of the circle passing through them is.2015 (SB/SX)
  29. 29The angle bisectors and of a triangle are divided by the incentre in the rators and respectively. Then the ratio in which I divides the angl2014 (SA)
  30. 30In a triangle with is a point on such that . If and , then BP : PC is2014 (SA)
  31. 31Let be a triangle such that . Let be the midpoint of and be a point on such that is perpendicular to . If then the ratio equals :2014 (SB/SX)
  32. 32The number of values of for which there is an isosceles triangle with sides of length and is2013 (SA)
  33. 33In an acute-angled triangle , the altitudes from when extended intersect the circumcircle again at points , respectively. If then equals2013 (SA)
  34. 34Let be the diameter of a semicircle with centre . Let be a variable point on the semicircle and another point on the semicircle such that is2013 (SB/SX)
  35. 35Let be an acute-angled triangle and let be the midpoint of . If , then equals2013 (SB/SX)
  36. 36In triangle , let and be the internal angle bisectors with D, E and on the sides and respectively. Suppose and concur at and are concyclic, 2012 (SA)
  37. 37In a triangle , it is known that . Suppose is the mid- point of and . Then the area of the triangle is2012 (SA)
  38. 38Let be the orthocenter of an acute - angled triangle and be its circumcenter. Then2012 (SB/SX)
  39. 39In the adjoining figure . If , then2011 (SA)
  40. 40Let be a triangle with . Let be the bisector of with on . Suppose and the area of the triangle is . Then the length of in is equal to2011 (SA)
  41. 41In triangle , we are given that and . Then the measure of the angle is -2011 (SB/SX)
  42. 42Let be an equilateral triangle, let KLMN be a rectangle with on on and on . Suppose AN and the area of triangle BKN is The area of the trian2010 (SB/SX)
  43. 43Let be a triangle and be a point inside such that . The ratio of the area of triangle to that of is-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Properties of Triangles?

This chapter includes 43 questions compiled from KVPY papers spanning 2010 to 2020.

2.Are these questions only from KVPY, or from other exams too?

These are KVPY questions specifically for the Properties of Triangles chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Properties of Triangles an important chapter for KVPY Mathematics?

Properties of Triangles has appeared in 11 of the 11 years of KVPY papers covered here, with 43 questions across 20 papers - about 2 per paper it appears in.