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Properties of Triangles — JEE Main & Advanced Mathematics PYQs

61 previous year questions from Properties of Triangles with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

61 questionsMathematicsSolutions on every page

In a triangle ABC , BC =7, AC =8, AB = N and A = 2 3 . If 49 (3 C )+42= m n , where gcd ( m , n )=1 , then m + n is equal to________

JEE Main 2024 Solution View → 2

Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is π 2 and whose sides are in arithmetic progression. Suppose that

JEE Advanced 2023 Solution View → 3

Consider an obtuse angled triangle A B C in which the difference between the largest and the smallest angle is π 2 and whose sides are in arithmetic progression. Suppose that

JEE Advanced 2023 Solution View → 4

For a triangle A B C , the value of cos 2 A + cos 2 B + cos 2 C is least. If its inradius is 3 and incentre is M , then which of the following is NOT correct?

JEE Main 2023 Solution View → 5

Let A B C be the triangle with A B = 1 , A C = 3 and ∠ B A C = π 2 . If a circle of radius r > 0 touches the sides A B , A C and also touches internally the circumci

JEE Advanced 2022 Solution View → 6

Let a , b and c be the length of sides of a triangle A B C such that a + b 7 = b + c 8 = c + a 9 . If r and R are the radius of incircle and radius of circumcircle of the triangle

JEE Main 2022 Solution View → 7

Consider a triangle P Q R having sides of lengths p , q and r opposite to the angles P , Q and R , respectively. Then which of the following statements is (are) TRUE?

JEE Advanced 2021 Solution View → 8

In a triangle A B C , let A B = 23 , B C = 3 and C A = 4 . Then the value of cot A + cot C cot B is

JEE Advanced 2021 Solution View → 9

Let sin A sin B = sin ( A - C ) sin ( C - B ) , where A , B , C are angles of a triangle A B C . If the lengths of the sides opposite these angles are a , b , c respectively, then

JEE Main 2021 Solution View → 10

Let in a right angled triangle, the smallest angle be θ . If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then sin θ is equal

JEE Main 2021 Solution View → 11

If in a triangle A B C , A B = 5 units, ∠ B = cos - 1 3 5 and radius of circumcircle of ∆ A B C is 5 units, then the area (in sq. units) of Δ A B C is:

JEE Main 2021 Solution View → 12

In ΔABC , the lengths of sides A C and A B are 12 cm and 5 cm , respectively. If the area of ∆ ABC is 30 cm 2 and R and r are respectively the radii of circumcircle and

JEE Main 2021 Solution View → 13

Let x , y and z be positive real numbers. Suppose x , y and z are the lengths of the sides of a triangle opposite to its angles X , Y and Z respectively. If tan X 2 + tan Z 2 = 2 y

JEE Advanced 2020 Solution View → 14

Suppose that the side lengths of a triangle are three consecutive integers and one of the angles is twice another. The number of such triangles is/are

NTA Abhyas JEE Main 2020 Solution View → 15

The inradius of the triangle having sides 26, 28, 30 units is

NTA Abhyas JEE Main 2020 Solution View → 16

The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60 o . If the area of the quadrilateral is 4 3 sq. units, then the

NTA Abhyas JEE Main 2020 Solution View → 17

Two sides of a triangle are given by the roots of the equation x 2 - 2 3 x + 2 = 0 and the angle between the sides is π 3 . The perimeter of the triangle is

NTA Abhyas JEE Main 2020 Solution View → 18

Two medians drawn from acute angles vertices of a right angled triangle intersects at an angle π 6 . If the length of the hypotenuse of the triangle is 3 units, then area of the tr

NTA Abhyas JEE Main 2020 Solution View → 19

In a non-right-angled triangle Δ P Q R , let p , q , r denote the lengths of the sides opposite to the angles at P , Q , R respectively. The median from R meets the side P Q a

JEE Advanced 2019 Solution View → 20

The angles A , B & C of a ∆ A B C are in A . P . and a : b = 1 : 3 . If c = 4 c m , then the area (in s q . c m ) of this triangle is:

JEE Main 2019 Solution View → 21

If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

JEE Main 2019 Solution View → 22

Given b + c 11 = c + a 12 = a + b 13 for a ABC with usual notation. If A = B = C , then the ordered triad ( , , ) has a value

JEE Main 2019 Solution View → 23

With the usual notation in ∆ A B C , if ∠ A + ∠ B = 120 ° , a = 3 + 1 units and b = 3 - 1 units, then the ratio ∠ A : ∠ B is

JEE Main 2019 Solution View → 24

In a triangle P Q R , l e t ∠ P Q R = 30 o and the sides P Q a n d Q R have lengths 10 3 a n d 10 , respectively. Then, which of the following statement(s) is (are) TRUE?

JEE Advanced 2018 Solution View → 25

In a triangle A B C , coordinates of A are 1 , 2 and the equations of the medians through B and C are respectively, x + y = 5 and x = 4 . Then area of Δ A B C (in sq. units) i

JEE Main 2018 Solution View → 26

Let the orthocentre and centroid of a triangle be A - 3 , 5 and B 3 , 3 respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment A

JEE Main 2018 Solution View → 27

Paragraph: Let O be the origin, and O X , O Y , O Z be three unit vectors in the directions of the sides Q R , R P , P Q , respectively, of a triangle P Q R . Question: If the tria

JEE Advanced 2017 Solution View → 28

In a ∆ X Y Z let x , y , z , be the lengths of sides opposite to the angles, X , Y , Z , respectively and 2 s = x + y + z . If s - x 4 = s - y 3 = s - z 2 and area of incircl

JEE Advanced 2016 Solution View → 29

Column I Column II A In a triangle ∆ X Y Z let a , b and c be the lengths of the angles X , Y and Z , respectively. If 2 a 2 − b 2 = c 2 and λ = sin X − Y si

JEE Advanced 2015 Solution View → 30

In a triangle the sum of two sides is x and the product of the same two sides is y. If x 2 - c 2 = y , (where c is the third side of the triangle) then the ratio of the inradius to

JEE Advanced 2014 Solution View → 31

Let A (2,3,5), B (-1,3,2) and C ( , 5, ) be the vertices of a ABC . If the median through A is equally inclined to the coordinate axes, then:

JEE Main 2014 Solution View → 32

In a ∆ P Q R , P is the largest angle and cos P = 1 3 . Further the incircle of the triangle touches the sides P Q , Q R and R P at N , L and M respectively, such that the le

JEE Advanced 2013 Solution View → 33

If the extremities of the base of an isosceles triangle are the points (2 a, 0) and (0, a) and the equation of one of the sides is x=2 a , then the area of the triangle, in square

JEE Main 2013 Solution View → 34

On the sides AB , BC , CA of a ABC , 3,4,5 distinct points (excluding vertices A , B , C ) are respectively chosen. The number of triangles that can be constructed using these chos

JEE Main 2013 Solution View → 35

If two vertices of an equilateral triangle are A (-a, 0) and B(a, 0), a>0 , and the third vertex C lies above x -axis then the equation of the circumcircle of ABC is :

JEE Main 2013 Solution View → 36

Let P Q R be a triangle of area with a=2, b= 7 2 and c= 5 2 ; where a, b , and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. The

JEE Advanced 2012 Solution View → 37

If three distinct points A, B, C are given in the 2dimensional coordinate plane such that the ratio of the distance of each one of them from the point (1,0) to the distance from (-

JEE Main 2012 Solution View → 38

If in a triangle A B C, b+c 11 = c+a 12 = a+b 13 , then A is equal to

JEE Main 2012 Solution View → 39

In a PQR , if 3 P +4 Q =6 and 4 Q +3 P =1 , then the angle R is equal to

JEE Main 2012 Solution View → 40

Consider a triangle A B C and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a=6, b=10 and the area of the triangle is 15 3 .

JEE Advanced 2010 Solution View → 41

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the

JEE Advanced 2010 Solution View → 42

Let A B C be a triangle such that A C B= 6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a=x^2+x+1, b=x^2-1 an

JEE Advanced 2010 Solution View → 43

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

JEE Main 2010 Solution View → 44

Let A B C and A B C^ be two non-congruent triangles with sides A B=4 , A C=A C^ =2 2 and angle B=30^ . The absolute value of the difference between the areas of these triangles is

JEE Advanced 2009 Solution View → 45

In a A B C with fixed base B C , the vertex A moves such that B+ C=4 ^2 A 2 . If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C respec

JEE Advanced 2009 Solution View → 46

Let O(0,0), P(3,4) and Q(6,0) be the vertices of the O P Q . The point R inside the O P Q is such that the O P R, P Q R, O Q R are of equal area. The coordinates of R are

JEE Advanced 2007 Solution View → 47

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q

JEE Advanced 2007 Solution View → 48

Inradius of a circle which is inscribed in an isosceles triangle one of whose angle is 2 / 3 , is 3 , then area of triangle is

JEE Advanced 2006 Solution View → 49

If a, b and c are the sides of a A B C such that x^2-2(a+b+c) x+3 (a b+b c+c a)=0 has real roots, then

JEE Advanced 2006 Solution View → 50

Internal bisector of A of A B C meets side B C at D . A line drawn through D perpendicular to A D intersects the side A C at E and side A B at F . If a, b and c represent sides of

JEE Advanced 2006 Solution View → 51

Match the following.

JEE Advanced 2006 Solution View → 52

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by

JEE Main 2006 Solution View → 53

ABC is a triangle. Forces P , Q , R acting along I A, I B and I C respectively are in equilibrium, where I is the incentre of A B C . Then P: Q: R is

JEE Main 2005 Solution View → 54

In a triangle PQR , R = 2 . If ( P 2 ) and ( Q 2 ) are the roots of a x^2+b x+c=0, a 0 then

JEE Main 2005 Solution View → 55

In a triangle ABC , let C = 2 . If r is the inradius and R is the circumradius of the the triangle A B C , then 2(r+R) equals

JEE Main 2005 Solution View → 56

The sides of a triangle are , and 1+ for some 0 < < 2 . Then the greatest angle of the triangle is

JEE Main 2004 Solution View → 57

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

JEE Main 2003 Solution View → 58

In a triangle ABC , medians AD and BE are drawn. If AD =4, DAB = 6 and ABE = 3 , then the area of the ABC is

JEE Main 2003 Solution View → 59

If in a triangle ABC a ^2 ( C 2 )+ c ^2 ^2 ( A 2 )= 3 ~b 2 , then the sides a , b and c

JEE Main 2003 Solution View → 60

The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

JEE Main 2002 Solution View → 61

In a triangle with sides a, b, c, r₁>r₂>r₃ (which are the ex-radii) then

JEE Main 2002 Solution View →

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