JEE MAIN Properties Of Triangle Previous Year Questions (PYQs) – Page 1 of 3
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If the orthocentre of the triangle whose vertices are $(1,2)$, $(2,3)$ and $(3,1)$ is $(\alpha,\beta)$, then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:
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Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocenter is at the origin, then its third vertex lies in which quadrant:
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The $x$-coordinate of the incentre of the triangle that has the coordinates of
mid points of its sides as $(0,1)$, $(1,1)$ and $(1,0)$ is :
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If $(a,b)$ be the orthocentre of the triangle whose vertices are $(1,2)$, $(2,3)$ and $(3,1)$, and
$I_1=\displaystyle\int_a^b x\sin(4x-x^2)\,dx,\ \ I_2=\displaystyle\int_a^b \sin(4x-x^2)\,dx,$
then $36\,\dfrac{I_1}{I_2}$ is equal to:
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The equations of the sides $AB$, $BC$ and $CA$ of a triangle $ABC$ are $2x+y=0$, $x+py=39$ and $x-y=3$ respectively and $P(2,3)$ is its circumcentre. Then which of the following is NOT true?
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A circle is inscribed in an equilateral triangle of side $12$. If the area and perimeter of any square inscribed in this circle are $m$ and $n$, respectively, then $m+n^{2}$ is equal to:
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Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q$\left(k_{1}, k_{2}\right)$, then $k_{1}+k_{2}$ is equal to :
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Let $A(\alpha,-2)$, $B(\alpha,6)$ and $C\!\left(\dfrac{\alpha}{4},-2\right)$ be vertices of $\triangle ABC$.
If $\left(5,\dfrac{\alpha}{4}\right)$ is the circumcentre of $\triangle ABC$, then which of the following is NOT correct about $\triangle ABC$?
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Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $\Delta$PQR is :
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If $P(6,1)$ is 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:
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