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

Three villages \(P, Q,\) and \(R\) are located in such a way that the distances are \(PQ=13\) km, \(QR=14\) km, and \(RP=15\) km (see 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?

An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is {NOT} possible?