List of top General Aptitude Questions on Geometry asked in GATE XE, GATE CS

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72º anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. Moves forward by 10 cm.
2. Turns 144º clockwise.
The pattern made by the trace left behind by the ant is:

If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then $\cos \theta =$

A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?