List of top General Aptitude Questions on Geometry asked in GATE AG

Circles \( C_1 \), \( C_2 \), and \( C_3 \), with centers \( O_1 \), \( O_2 \), and \( O_3 \), and radii \( r_1 \), \( r_2 \), and \( r_3 \), respectively, touch each other as shown in the following figure.

Given \( r_1 = 2 \) cm, \( r_2 = 1 \) cm and the angle \( \angle O_1 O_3 O_2 \) is \( 90^{\circ} \), \( r_3 = \) _____ cm.

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT? 
Note: The figure shown is representative


 

A line of symmetry is a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of \(16\) unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both \(PQ\) and \(MN\) form lines of symmetry? (The figure is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and not allowed to overlap.
In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\) cm, \(PT = 4\) cm and \(PV = 5\) cm. What is the length of \(RS\) in cm? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}