Embibe Experts Solutions for Exercise 1: SAT 2019

Two circles, both of radii ‘$a$’ touch each other and each of them touches internally a circle of radius $2a$. Then the radius of the circle which touches all the three circles is

Let $A(-5,5), B(4,-5) \mathrm{and} C(4,5)$ be the vertices of the triangle $ABC.$ If a circle passes through the vertices of $△ABC$ then the area (in sq. units) lying inside the circle but outside the $△ABC$ is

Let $G$ be the centroid of the triangle $ABC$ in which the angle $C$ is obtuse. Let $AD$ and $CF$ are the medians from $A$ and $C$ on the sides $BC$ and $AB$ respectively. If the four points $B,D,G$ and $F$ are concyclic, then $\frac{BC}{AC}$

Let $ABC$ be a triangle with sides $a,b,c$. Then lengths of medians of the triangle formed by the medians of the triangle $ABC$ are

Let $ABCD$ be a square of side $20 cm$. The area of the square $PQRS$ (in $c{m}^2$) interior to $ABCD$, shown in the figure is

Let $D$ be a point on the side $BC$ of a triangle $ABC$ such that $\angle \mathrm{ADC}=\angle \mathrm{BAC}$. If $AC=21 cm$, then the side of an equilateral triangle whose area is equal to the area of the rectangle with sides $BC$ and $DC$ is

In the given figure, $ABCD$ is a rectangle. Then the area of the shaded region is

In quadrilateral $ABCD$, $\angle ABC+\angle DCB=90°$ and $ADEF$ is a square constructed on side $AD$ in the exterior of the quadrilateral $ABCD$. If $BC=10 \mathrm{cm},AC=9 \mathrm{cm}\text{ and }BD=8 \mathrm{cm}$, then the area (In ${\mathrm{cm}}^2$) of the square $ADEF$ lies between.