K. C. Sinha Solutions for Chapter: Properties of Triangles, Exercise 1: EXERCISE

In a triangle $ABC,$ $\tan A+\tan B+\tan C=10$ then the triangle is

If in a triangle $ABC,\frac{s-a}{11}=\frac{s-b}{12}=\frac{s-c}{13}$. Then $429{\cot }^2\frac{A}{2}$ is equal to...

If in a triangle $ABC, Rr\left(\sin A+\sin B+\sin C\right)=96$, then the area of the triangle $ABC$ is...

If in a triangle $ABC,a$ is the arithmetic mean and $b,c$ are the geometric means between any two positive real numbers, $k=\frac{b+c}{a}\left[\frac{\sin B}{\sin C}+\frac{\sin C}{\sin B}-1\right]$, then $90k^3+87k^2+30k$ is equal to...

The sides of a quadrilateral are $3,4,5$ and $6\mathrm{cms}$. The sum of a pair of opposite angles is $120°$. Then $5\sqrt{30}$ times the area of the quadrilateral is...

Three circles touch one another externally. The tangents at their point of contact meet in a point whose distance from the point of contact is $25$. The ratio of the product of radii to the sum of radii of the circles is...

In a triangle $ABC,a:b:c=4:5:6$, then $56$ times the ratio of the radius of the circumcircle to that of the incircle is...