SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-8
question_answer
If all the sides of a parallelogram touch a circle, then the parallelogram is a
A) square
B) rectangle
C) rhombus
D) trapezium
Correct Answer:
C
Solution :
ABCD is a parallelogram such that its sides touch a circle with centre 0. The tangents to a circle from an exterior point are equal in length. \[\therefore \] AP = AS; BP = BQ: CR = CQ and DR = DS. Adding all, AP + BP + CR + DR = AS + BQ + CQ+DS \[\Rightarrow \](AP + BP) + (CR + DR) \[\Rightarrow \] (AS + DS) + (BQ + CQ) \[\Rightarrow \]AB+CD=AD+BC \[\Rightarrow \]2AB = 2 BC \[\Rightarrow \] AB = BC \[\Rightarrow \]AB=BC=CD=AD Hence, ABCD is a rhombus.