If the two angles on the base of a triangle are $22.5^o$ and $112.5^o$,then the ratio of the height of the triangle to the length of the base is

Let $ABC$ be a triangle and let $D$ be the mid-point of $BC$. Suppose $\cot (\angle CAD) : \cot (\angle BAD) = 2 : 1$. If $G$ is the centroid of $\triangle ABC$,then the measure of $\angle BGA$ is (in $^{\circ}$)

With usual notation in a $\Delta ABC$,$\left( \frac{1}{r_1} + \frac{1}{r_2} \right) \left( \frac{1}{r_2} + \frac{1}{r_3} \right) \left( \frac{1}{r_3} + \frac{1}{r_1} \right) = \frac{K R^3}{a^2 b^2 c^2}$ where $K$ has the value equal to

If in a triangle the angles are in $A.P.$ and $b:c = \sqrt{3}:\sqrt{2}$,then $\angle A$ is equal to .....$^o$.

Let $PQR$ be a triangle of area $\Delta$ with $a=2, b=\frac{7}{2}$ and $c=\frac{5}{2}$,where $a, b$ and $c$ are the lengths of the sides of the triangle opposite to the angles at $P, Q$ and $R$ respectively. Then $\frac{2 \sin P-\sin 2P}{2 \sin P+\sin 2P}$ equals

If $A, B, C, D$ are angles of a cyclic quadrilateral,then $\cos A + \cos B + \cos C + \cos D$ is equal to