In a triangle $ABC$,$AD$ is the altitude from $A$. Given $b > c$,$\angle C = 23^o$ and $AD = \frac{abc}{b^2 - c^2}$,then $\angle B = \dots^o$.

In a $\triangle ABC$,the value of $\Sigma(b+c) \tan \frac{A}{2} \tan \left(\frac{B-C}{2}\right)$ is equal to

If the equation $\sin^4 x - (p+2) \sin^2 x - (p+3) = 0$ has a solution, then $p$ must lie in the interval:

Let $\alpha$ and $\beta$ be two distinct roots of $a \cos \theta + b \sin \theta = c$, where $a, b, c$ are three real constants and $\theta \in [0, 2\pi]$. Then, $\alpha + \beta$ is also a root of the same equation, if

In a $\triangle ABC$, $\tan A$ and $\tan B$ are the roots of the equation $pq(x^{2}+1) = r^{2}x$. Then, $\triangle ABC$ is:

In $\triangle ABC$, right-angled at $A$, the circumradius, inradius, and radius of the excircle opposite to $A$ are respectively in the ratio $2:5:\lambda$. Then the roots of the equation $x^2-(\lambda-5)x+(\lambda-6)=0$ are: