If the vertices of a triangle are $$(-2,3),(6,-1)$$ and $$(4,3)$$, then the co-ordinates of the circumcentre of the triangle are

In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest an...

If the angles of a triangle are in the ratio $$4: 1: 1$$, then the ratio of the longest side to its perimeter is

If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$$, then

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6$$ and $$\mathrm{B}=\sin...

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{c}=4$$, then value of $$(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}$$ i...

If one side of a triangle is double the other and the angles opposite to these sides differ by $$60^{\circ}$$, then the triangle is

In $$\triangle \mathrm{PQR}, \sin \mathrm{P}, \sin \mathrm{Q}$$ and $$\sin \mathrm{R}$$ are in A.P., then

Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. Then $$\frac{(\mathrm{A}(\tri...

In $$\triangle \mathrm{ABC}$$, with usual notations, $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{2}$$, if $$\tan \left(\frac{A}{2}\right)$$ and $$\tan \...

Two sides of a triangle are $$\sqrt{3}+1$$ and $$\sqrt{3}-1$$ and the included angle is $$60^{\circ}$$, then the difference of the remaining angles is...

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of ang...

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio.