Distances of the Centres of a Triangle from Its Vertices and Sides

Find the distance of the centroid from the sides of a triangle.

Value of $\frac{\mathrm{a}}{\mathrm{p}}+\frac{\mathrm{b}}{\mathrm{q}}+\frac{\mathrm{c}}{\mathrm{r}}$ is equal to (where $\mathrm{a},\mathrm{b},\mathrm{c}$ are length of sides $\mathrm{BC}$, $\mathrm{CA}$ and $\mathrm{AB}$ respectively)

In an acute-angled triangle $ABC,$ points $D, E,$ and $F$ are the feet of the perpendiculars from $A, B,$ and $C$ onto $BC, AC,$and $AB,$ respectively. Suppose $\sin A=\frac{3}{5}$ and $BC=39$ units. Find the length of $AH,$ where $H$ is the intersection $AD$ with $BE.$

Value of $\frac{\mathrm{a}}{\mathrm{p}}+\frac{\mathrm{b}}{\mathrm{q}}+\frac{\mathrm{c}}{\mathrm{r}}$ is equal to (where $\mathrm{a},\mathrm{b},\mathrm{c}$ are length of sides $\mathrm{BC}$, $\mathrm{CA}$ and $\mathrm{AB}$ respectively)

Consider a $∆ABC$ and $D, E$ and $F$ are the foot of the perpendicular drawn from the vertices $A, B$ and $C$ respectively. Let $H$ be the orthocentre of the triangle $ABC$. Then the value of $R$ is:

Consider a $∆ABC$ and $D, E$ and $F$ are the foot of the perpendicular drawn from the vertices $A, B$ and $C$ respectively. Let $H$ be the orthocentre of the triangle $ABC$. Then the value of $\frac{\cos A·\cos B·\cos C}{{\cos }^{2}A+{\cos }^{2}B+{\cos }^{2}C}$ is:

For a triangle $ABC,R=\frac{5}{2}$ and r=1. Let D,E and F be the feet of the perpendicular from incentre I to BC, CA and AB, respectively. Then the value of $\frac{\left(IA\right)\left(IB\right)\left(IC\right)}{\left(ID\right)\left(IE\right)\left(IF\right)}$ is equal to _________

In $\Delta ABC, b=12$ units, $c=5$ units and $\Delta =30 \mathrm{sq}.$ units. If $d$ is the distance between vertex $A$ and incentre of the triangle, then the value of $d^2$ is

Cotyledons are also called-

In a ∆ABC, the line joining circumcenter to the incenter is parallel to BC, then value of cos B + cos C is

If in $\mathrm{\Delta }ABC$, the line joining the circum-centre and the in-centre is parallel to $BC$, then-

In an acute angled triangle $ABC$, the ratios of distances of orthocentre from the sides $AB,BC$ and $CA$ is, respectively

If the distances of the vertices of a triangle from the point of contact of the incircle with the sides be $\alpha , \beta , \gamma$ then $r$ is equal to (where $r=$inradius)

$ABC$is an acute - angled triangle with circumcentre $\text{'}O\text{'}$ and orthocentre $H.$If $AO=AH$, then angle $A$ is

In a triangle with sides a, b, c, r₁ > r₂ > r₃ (which are the ex-radii) then