Circumcentre and Orthocentre - Practice Questions & MCQ

Two vertices of a triangle are (0,2) and (4,3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

The radical centre of three circles described on the three sides of a triangle as diameter is the 

Let the position vectors of the vertices $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a triangle be $2 \hat{\imath}+2 \hat{\jmath}+\hat{k}, \hat{\imath}+2 \hat{\jmath}+2 \hat{k}$ and $2 \hat{\imath}+\hat{\jmath}+2 \hat{k}$ respectively. Let $\ell_1, \ell_2$ and $\ell_3$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{CA}$ respectively, then $\ell_1^2+\ell_2^2+\ell_3^2$ equals:

Consider the triangle OAB where $\mathrm{O}=(0,0), \mathrm{B}=(3,4)$. If the orthocentre of a triangle is $\mathrm{H}(1,4)$ then coordinate of A is

If ABC is a triangle with vertices $(2,2) ;(\sqrt{5}, \sqrt{3})$ and $(\sqrt{2}, \sqrt{6})$ then radius of circum circle is

If all the altitudes of a triangle passes through a unique point , then this point is called 

The point of intersection of the perpendicular bisectors of the sides of a triangle is called 

What is a circumcircle ? 

If $P(-3,-4)$ and $Q(3,4)$ are circumcenter and orthocenter of $\triangle A B C$ and $x+y+7=0$ is equation of side AB then

What is the distance of an incentre I(2,-1) from side AB of a $\Delta ABC$ , which circumscriber this incircle of radius 5 units ?