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JEE Properties of Triangles PYQs with Solutions

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

61 questionsMathematics2002–2024Answers + solutions

About Properties of Triangles PYQs

Properties of Triangles has 61 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 61 questions in this list come from JEE Main (31), JEE Advanced (25) and NTA Abhyas JEE Main (5), spanning 2002 to 2024. Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Properties of Triangles PYQs with Solutions

About Properties of Triangles PYQs

Questions by year (this list)

Properties of Triangles questions with solutions

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

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is (π)/(2) and whose sides are in arithmetic progression. Suppose that

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is (π)/(2) and whose sides are in arithmetic progression. Suppose that

For a triangle ABC , the value of cos2A + cos2B + cos2C is least. If its inradius is 3 and incentre is M , then which of the following is NOT correct?

Let ABC be the triangle with AB = 1, AC = 3 and ∠ BAC = (π)/(2) . If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle

Let a, b and c be the length of sides of a triangle ABC 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

Consider a triangle PQR 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?

In a triangle ABC , let AB = 23 , BC = 3 and CA = 4 . Then the value of (cotA + cotC)/(cotB) is

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

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 sinθ is equal to:

If in a triangle ABC, AB = 5 units, ∠ B = ^ - 1 ((3)/(5)) and radius of circumcircle of ∆ ABC is 5 units, then the area (in sq. units) of is:

In Δ ABC, the lengths of sides AC and AB are 12cm and 5cm, respectively. If the area of ∆ ABC is 30 cm ^ 2 and R and r are respectively the radii of circumcircle and incircle of Δ

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) =

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

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

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

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

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

In a non-right-angled triangle , 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 PQ at S, the

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

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:

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

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

In a triangle PQR, let∠PQR = 30 ^ o and the sides PQandQR have lengths 10 3 and10 , respectively. Then, which of the following statement(s) is (are) TRUE?

In a triangle ABC , 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 (in sq. units) is :

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

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

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

Column I Column II (A) In a triangle ∆ XYZ 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))/(sinZ) then

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

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

In a ∆ PQR , P is the largest angle and cosP = (1)/(3) . Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of

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

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 chosen

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 :

Let P Q R be a triangle of area Δ 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

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

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

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

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 .

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

Let A B C be a triangle such that ∠ A C B=(π)/(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

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

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

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

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

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

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

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

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

Match the following.

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

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

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

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

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

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

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

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

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

In a triangle with sides a, b, c, r_1>r_2>r_3 (which are the ex-radii) then

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