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Q. 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 :
(1) $2+\sqrt{2}$
(2) $2-\sqrt{2}$
(3) $1+\sqrt{2}$
(4) $1-\sqrt{2}$

**[JEE-MAIN 2013]**
Q. Let $\mathrm{A}(-3,2)$ and $\mathrm{B}(-2,1)$ be the vertices of a triangle ABC. If the centroid of this triangle lies on the line $3 x+4 y+2=0,$ then the vertex $\mathrm{C}$ lies on the line:
(1) 4

*x*+ 3y + 5 = 0 (2) 3*x*+ 4y + 5 = 0 (3) 3*x*+ 4y + 3 = 0 (4) 4*x*+ 3y + 3 = 0**[JEE-MAIN Online 2013]**
Q. Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :
(1) $\left(2, \frac{1}{2}\right)$
( 2)$\left(2,-\frac{1}{2}\right)$
(3) $\left(1, \frac{3}{4}\right)$
(4) $\left(1,-\frac{3}{4}\right)$

**[JEE(Main)-2017]**
Q. 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 AC as diameter, is:
(1) $2 \sqrt{10}$
(2) $3 \sqrt{\frac{5}{2}}$
(3) $\frac{3 \sqrt{5}}{2}$
(4) $\sqrt{10}$

**[JEE(Main)-2018]**
less quantity