Centres of a triangle

JEE Main Mathematics · Straight Lines · 23 questions, latest first

• In an equilateral triangle P Q R, let the vertex P be at (3,5) and the side Q R be along the line x+y=4. If the orthocentre of…20265 April, Shift 1 · Q11
• Let A, B be points on the two half-lines x-√3|y|=α, α>0 at a distance of α from their point of intersection P. The line segment…20264 April, Shift 2 · Q23
• Let the vertex A of a triangle A B C be (1,2), and the mid-point of the side A B be (5,-1). If the centroid of this triangle is…20264 April, Shift 1 · Q12
• Let the mid points of the sides of a triangle ABC be (5/2, 7),(5/2, 3) and (4, 5). If its incentre is (h, k), then 3 h+k is equal…20262 April, Shift 1 · Q9
• Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+2 √2 y=4. If the co-ordinates of…202628 January, Shift 1 · Q10
• Among the statements (S1): If A(5, -1) and B(-2,3) are two vertices of a triangle, whose orthocentre is (0, 0), then its third…202622 January, Shift 2 · Q13
• If the orthocenter of the triangle formed by the lines y=x+1, y=4 x-8 and y=m x+c is at (3, -1), then m - c is:20257 April, Shift 2 · Q11
• Let ABC be the triangle such that the equations of lines AB and AC be 3 y-x=2 and x+y=2, respectively, and the points B and C lie…20257 April, Shift 1 · Q11
• Let the three sides of a triangle are on the lines 4 x-7 y+10=0, x+y=5 and 7 x+4 y=15. Then the distance of its orthocentre from…20254 April, Shift 1 · Q10
• Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b) be 35 square units. If its orthocenter and centroid are O(2,…202523 January, Shift 1 · Q9
• Let A(6,8), B(10 cos α,-10 sin α) and C(-10 sin α, 10 cos α), be the vertices of a triangle. If L(a, 9) and G(h, k) be its…202522 January, Shift 2 · Q22
• Two vertices of a triangle ABC are A(3,-1) and B(-2,3), and its orthocentre is P(1,1). If the coordinates of the point C are (α,…20249 April, Shift 2 · Q14
• If the orthocentre of the triangle formed by the lines 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-1=0, is the centroid of another…20248 April, Shift 1 · Q29
• 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…20246 April, Shift 2 · Q15
• Let (5, a/4) be the circumcenter of a triangle with vertices A(a,-2), B(a, 6) and C(a/4,-2). Let α denote the circumradius, β…202429 January, Shift 1 · Q14
• If (α, β) is the orthocenter of the triangle ABC with vertices A(3,-7), B(-1,2) and C(4,5), then 9 α-6 β+60 is equal to202315 April, Shift 1 · Q12
• Let (α, β) be the centroid of the triangle formed by the lines 15 x-y=82,6 x-5 y=-4 and 9 x+4 y=17. Then α+2 β and 2 α-β are the…202313 April, Shift 2 · Q12
• 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…20238 April, Shift 2 · Q12
• Let C(α, β) be the circumcenter of the triangle formed by the lines 4 x+3 y=69, 4 y-3 x=17, and x+7 y=61. Then (α-β)^2+α+β is…20238 April, Shift 1 · Q13
• If the orthocentre of the triangle, whose vertices are (1,2),(2,3) and (3,1) is (α, β), then the quadratic equation whose roots…20231 February, Shift 1 · Q73
• A triangle is formed by the tangents at the point (2,2) on the curves y^2=2 x and x^2+y^2=4 x, and the line x+y+2=0. If r is the…202329 January, Shift 2 · Q89
• The equations of the sides AB and AC of a triangle ABC are (λ+1) x+λ y=4 and λ x+(1-λ) y+λ=0 respectively. Its vertex A is on the…202324 January, Shift 2 · Q75
• The equations of the sides AB, BC and CA of a triangle ABC are: 2 x+y=0, x+p y=21 a,(a ≠ 0) and x-y=3 respectively. Let P(2, a)…202324 January, Shift 2 · Q89