Three circles each of diameter $2x$ are drawn inside an equilateral triangle with perimeter $3y$ such that each circle touches the other two and also other two sides then the ratio of radius of a circle to side of a triangle is _____.

In the given figure, $ABC$ is an isosceles triangle with $AB = AC$. If $AE = AF$ and $\angle BAE=40°$, then the measure of the angle $FEC$ is

If $\sin \theta =\frac{12}{13}$, find the value of $\cos \theta \& \tan \theta .$

The rod $AC$ of a TV disc antenna is fixed at right angles to the wall $AB$ and a rod $CD$ is supporting the disc as shown in the figure. If $AC=1.5 \mathrm{m}$ long and $CD=3 \mathrm{m}$, find $\sec \theta +\mathrm{cosec}\theta$

Let $ABCD$ be a square. An arc of a circle with $A$ as centre and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB, S$ on $AD, Q$ and $R$ on arc $BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then, $\frac{\text{ area }PQRS}{\text{ area }ABCD}$ is

The angles of a quadrilateral are in the ratio $3:5:7:9$. Find the measure of each of these angles.

The three angles of a quadrilateral are $76°, 54° \mathrm{and} 108°$. Find the measure of the fourth angle.

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is a

The angles of a quadrilateral are in the ratio $1:2:3:4$. Find the measure of each angle.