List of top Mathematics Questions on Triangles asked in JEE Main

Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABC and the same process is repeated infinitely many times. If P is the sum of perimeters and Q is be the sum of areas of all the triangles formed in this process, then:

In a triangle $ABC$, $BC = 7$, $AC = 8$, $AB = \alpha \in \mathbb{N}$ and $\cos A = \frac{2}{3}$. If \[ 49 \cos(3C) + 42 = \frac{m}{n}, \] where $\gcd(m, n) = 1$, then $m + n$ is equal to ________.

Let $P(\alpha, \beta, \gamma)$ be the image of the point $Q(3, -3, 1)$ in the line \[\frac{x - 0}{1} = \frac{y - 3}{1} = \frac{z - 1}{-1}\]and $R$ be the point $(2, 5, -1)$. If the area of the triangle $PQR$ is $\lambda$ and $\lambda^2 = 14K$, then $K$ is equal to:

If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.

Consider a triangle \( \triangle ABC \) having the vertices \( A(1, 2) \), \( B(\alpha, \beta) \), and \( C(\gamma, \delta) \) and angles \( \angle ABC = \frac{\pi}{6} \) and \( \angle BAC = \frac{2\pi}{3} \). If the points \( B \) and \( C \) lie on the line \( y = x + 4 \), then \( \alpha^2 + \gamma^2 \) is equal to \( \dots \).

If the orthocentre of the triangle formed by the lines 2x + 3y – 1 = 0, x + 2y – 1 = 0 and ax + by – 1 = 0, is the centroid of another triangle, whose circumecentre and orthocentre respectively are (3, 4) and (–6, –8), then the value of |a– b| is_____.

Let C(α, β) be the circumcenter of the triangle formed by the lines
4x+3y=69,
4y-3x=17, and
x+7y=61.
Then (α-β)²+α+β is equal to

Let the ellipse \(E : x^2 + 9y^2 = 9\) intersect the positive x- and y-axes at the points A and B respectively Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle which vertices A, P and the origin O is m/n , where m and n are coprime, then m – n is equal to 

If the line x = y = z intersects the line
xsinA+ysinB+zsinC-18=0=xsin2A+ysin2B+zsin2C-9,
where A, B, C are the angles of a triangle ABC, then 80\(\left( sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2} \right)\) is equal to ________.

If (a, β) is the orthocenter of the triangle ABC with vertices A(3, -7), B(-1, 2) and C(4, 5), then 9α-6β+60 is equal to

Let two vertices of triangle ABC be (2, 4, 6) and (0, –2, –5), and its centroid be (2, 1, –1). If the image of third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to

Let A (0, 1), B(1,1) and C (1,0) be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the parabola y² = 4ax passing through D is (α + β√3,0), where α and β are rational numbers, then α/β² is equal to

Let B and C be the two points on the line \(y + x = 0\) such that B and C are symmetric with respect to the origin. Suppose A is a point on \(y – 2x = 2\) such that \(\Delta ABC\) is an equilateral triangle. Then, the area of the \(\Delta ABC\) is

The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

A triangle is drawn inside a bounded region of y² = 2x and x = 24. Then maximum area of triangle is

Sides of a triangle are AB = 9, BC = 7, AC = 8. Then cos 3C equals to