Recent questions tagged triangles

There are $10$ points on a plane in such a way that $6$ of these points are collinear and other than these $6$ points, no set of $3$ or more points are collinear. The num...

The base of a triangle is $15 \mathrm{~cm}$. Two lines are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal area...

Consider the following right-angled triangle, in which the angle between the side $\text{AC}$ and $\text{CB}$ is a right angle. Let $a,b,c$ be the length of the sides $\t...

In the figure shown below, the circle has diameter $5$. Moreover, $AB$ is parallel to $DE.$ If $DE=3$ and $AB=6,$ what is the area of triangle $ABC?$

If a square of side $a$ and an equilateral triangle of side $b$ are inscribed in a circle then $a/b$ equals$\sqrt{2/3}$$\sqrt{3/2}$$3/ \sqrt{2}$$\sqrt{2}/3$

The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$b=\pm \sqrt{2}b$$b= – \sqrt{2}a$$b=a$

The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$a=\pm\sqrt{2}b$$b=-\sqrt{2}a$$b=a$

If $a,b,c$ are the sides of a triangle such that $a:b:c=1: \sqrt{3}:2$, then $A:B:C$ (where $A,B,C$ are the angles opposite to the sides of $a,b,c$ respectively) is$3:2:1...

Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+b-c)=ab,$ then the angle $C$ is$\frac{\pi}{6}$$\fra...

Let $A$ be the point of intersection of the lines $3x-y=1$ and $y=1$. Let $B$ be the point of reflection of the point $A$ with respect to the $y$-axis. Then the equation ...

Let us consider the length of the side of a square represented by $2y+3$. The length of the side of an equilateral triangle is $4y$. If the square and the equilateral tri...

Find the centroid of the triangle whose sides are given by the following equations:$$\begin{matrix} 4x & - & y & = &19 \\ x &- & y & = & 4 \\ x& + & 2y & = & -11 \end{mat...

Which of the triangles is an isosceles triangle having the three angles :$40^{\circ},50^{\circ},90^{\circ}$$30^{\circ},60^{\circ},90^{\circ}$$45^{\circ},45^{\circ},90^{\c...