List of top Mathematics Questions on Properties of Triangles

In a triangle \(ABC\), if \[ a=\sqrt3+1,\qquad b=\sqrt3-1 \] and \[ \angle C=60^\circ, \] then \(\cos(A-B)=\)

In a \(\triangle ABC\), if \(r_1=12,\; r_2=18,\; r_3=36\), then \(\Delta=\)

If sides of a triangle are \(6\) and \(3+3\sqrt3\) with included angle \(60^\circ\), then circumradius is

In triangle ABC, \[ (r_1-r)\cos\frac{B-C}{2} = ? \]

If \( (b - c)\cos \frac{A}{2} = k \sin \frac{B - C}{2} \), then \( \frac{k}{\sin A} = \) :

In a triangle ABC, if \( a = 2 \), \( \sin A = \frac{2}{3} \), \( B = \frac{\pi}{3} \), then \( \sqrt{5}b - 3c = \):

In a triangle \(ABC\), if \[ \tan\frac{A}{2}:\tan\frac{B}{2}:\tan\frac{C}{2}=1:2:3, \] then \[ \frac{a+3c}{b}= \]

In a triangle \(ABC\), if \[ r_2+r_3=2R, \] then \[ r+2r_2+2r_3-r_1= \]

In a triangle \(ABC\), if \[ r-r_1+r_2+r_3=2\sqrt2R,\qquad r+r_1-r_2+r_3=0 \] and \[ b=2\sqrt2 \] then \[ a+c= \]

In triangle ABC, if \[ \frac{a}{b+c}+\frac{c}{a+b}=1 \] and \[ s=r+a \] then \[ \sin A+\sin B+\sin C= \]

In a triangle ABC, $a=5, b=4$ and $\tan\frac{C}{2} = \sqrt{\frac{7}{9}}$, then its inradius r =

If the angular bisector of the angle A of the triangle ABC meets its circumcircle at E and the opposite side BC at D, then $DE\cos\frac{A}{2} =$

Two ships leave a port at the same time. One of them moves in the direction of E50$^\circ$N with a speed of 8 kmph and the other moves in the direction of S20$^\circ$E with a speed of 12 kmph. Then the distance between the ships at the end of 2 hours is (in km)

If $a=3, b=5, c=7$ are the sides of a triangle ABC, then its circumradius is

Let ABC be a triangle right angled at B. If a = 13 and c = 84, then r + R =

In a triangle ABC, if $c^2 - a^2 = b(\sqrt{3}c - b)$ and $b^2 - a^2 = c(c-a)$, then $\angle ACB =$