Properties of Triangles

In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$

In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$

In $\triangle A B C, b c-r_2 r_3=$

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$

In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$

In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$

If $H$ is orthocentre of $\triangle A B C$ and $A H=x ; B H=y$; $C H=z$, then $\frac{a b c}{x y z}=$

In a $\triangle A B C$, if $a=26, b=30, \cos c=\frac{63}{65}$, then $c=$

In $\triangle ABC$, $\cos A + \cos B + \cos C = $

In $\triangle A B C$, if $\cot \frac{A}{2}: \cot \frac{B}{2}: \cot \frac{C}{2}=3: 7: 9$, then $a: b: c=$

If $P_1, P_2$ and $P_3$ are the lengths of the altitudes drawn from the vertices $A, B$ and $C$ of $\triangle A B C$ respectively, then $\frac{\cos A}{P_1}+\frac{\cos B}{P_2}+\frac{\cos C}{P_3}=$

In $\triangle A B C$, if $\frac{1}{r_1}, \frac{1}{r_2}$ and $\frac{1}{r_3}$ are in arithmetic progression, then $r_2: r=$

If $\triangle A B C$ is a right angled isosceles triangle and $\angle C=90^{\circ}$, then $r: r_3=$

In $\triangle A B C$, if $\sin ^2 B=\sin C$ and $3 \cos ^2 B=2 \cos ^2 C$, then $\triangle A B C$ is

In $\triangle A B C$, if $a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$, then $a+c: b=$

In a \(\triangle A B C, a=6, b=5\) and \(c=4\), then \(\cos 2 A=\)

In a \(\triangle A B C\), if \(r_1=36, r_2=18\) and \(r_3=12\), then \(s=\)

In any \(\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\)

If the angles of a \(\triangle A B C\) are in the ratio \(1: 2: 3\), then the corresponding sides are in the ratio

In a \(\triangle A B C\), if \(a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=\)

If in a \(\triangle A B C, a=2, b=3\) and \(c=4\), then \(\tan (A / 2)=\)

In a \(\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=\)

Suppose \(\triangle A B C\) is an isosceles triangle with \(\angle C=90^{\circ}, A=(2,3)\) and \(B=(4,5)\). Then, the centroid of the triangle is

In a \(\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq\)

In a \(\triangle A B C\)
\((b+c) \cos A+(c+a) \cos B+(a+b) \cos C=\)

In a \(\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=\)

In a \(\triangle A B C, \frac{a}{b}=2+\sqrt{3}\) and \(\angle C=60^{\circ}\). Then, the measure of \(\angle A\) is

If \(a=2, b=3, c=4\) in a \(\triangle A B C\), then \(\cos C=\)

In a \(\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}\), then the triangle is

In \(\triangle A B C\), medians \(A D\) and \(B E\) are drawn. If \(A D=4, \angle D A B=\frac{\pi}{6}\) and \(\angle A B E=\frac{\pi}{3}\), then the area of \(\triangle A B C\) is

If in \(\triangle A B C, a \tan A+b \tan B=(a+b). \tan \left(\frac{A+B}{2}\right)\), then which of the following holds?

In \(\triangle A B C\), suppose the radius of the circle opposite to an angle \(A\) is denoted by \(r_1\), similarly \(r_2 \leftrightarrow\) angle \(B, r_3 \leftrightarrow\) angle \(C\). If \(r_1=2, r_2=3\) and \(r_3=6\), then what is $$(a,...

What is the value of \((a-b)^2 \cos ^2 \frac{c}{2}+(a+b)^2 \sin ^2 \frac{c}{2}\) is equal to

If D, E and F are respectively mid-points of AB, AC and BC in \(\Delta ABC\), then BE + AF is equal to

In \(\triangle A B C\), suppose the radius of the circle opposite to an \(\angle A\) is denoted by \(r_1\), similarly \(r_2 \leftrightarrow \angle B\) and \(r_3 \leftrightarrow \angle C\). If \(r\) is the radius of inscribed circle, then, w...

In \(\Delta ABC,A=75\Upsilon\) and \(B=45\Upsilon\), then the value of \(b+c\sqrt2\) is equal to

In a \(\Delta ABC\), if a = 3, b = 4 and \(\sin A=\frac{3}{4}\), then \(\angle CBA\) is equal to

In \(\triangle A B C\), suppose the radius of the circle opposite to an angle \(A\) is denoted by \(r_1\), similarly \(r_2 \leftrightarrow\) angle \(B, r_3 \leftrightarrow\) angle \(C\). If \(r_1=2, r_2=3, r_3=6\), what is the value of $$r_...