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Properties of Triangle

6 questions · Mathematics · JEE Main

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JEE Main
Mathematics
Properties of Triangle

Properties of Triangle

6 questions · Mathematics · JEE Main

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 orthocenter and centroid respectively, then $(5 a - 3 h + 6 k + 100 sin 2 α)$ …2025 · 22 Jan · Shift 2 · Q46 · Numerical
Let the area of a $△ P QR$ with vertices $P (5, 4), Q (- 2, 4)$ and $R (a, b)$ be 35 square units. If its orthocenter and centroid are $O (2, \frac{14}{5})$ and $C (c, d)$ respectively, then $c + 2 d$ is equal to2025 · 23 Jan · Shift 1 · Q43 · MCQ
Consider a triangle $ABC$ having the vertices $A (1, 2), B (α, β)$ and $C (γ, δ)$ and angles $∠ A B C = \frac{π}{6}$ and $∠ B A C = \frac{2 π}{3}$ . If the points $B$ and…2024 · 4 Apr · Shift 2 · Q54 · Numerical
In a triangle $ABC, BC = 7, AC = 8, AB = α \in N$ and $cos A = \frac{2}{3}$ . If $49 cos (3 C) + 42 = \frac{m}{n}$ , where $gcd (m, n) = 1$ , then $m + n$ …2024 · 6 Apr · Shift 2 · Q51 · Numerical
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 $(α, β)$ and the centre of the of the circle…2024 · 9 Apr · Shift 2 · Q35 · MCQ
Let $(5, \frac{a}{4})$ be the circumcenter of a triangle with vertices $A (a, - 2), B (a, 6)$ and $C (\frac{a}{4}, - 2)$ . Let $α$ denote the circumradius, $β$ denote the area and $γ$ …2024 · 29 Jan · Shift 1 · Q33 · MCQ