question_answer

The parallel chords of a circle with centre at C are such that PQ= 8 cm and RS = 16 cm. The chords lie on one side of centre and the distance between them is 4 cm. The radius of circle is

A)  \[3\sqrt{2}\]cm 

B)  \[2\sqrt{5}\]cm

C)  \[4\sqrt{5}\]cm 

D)  \[5\sqrt{5}\]cm

Correct Answer: C

Solution :

                        Radius = R cm                                     \[4=\sqrt{{{R}^{2}}-16}-\sqrt{{{R}^{2}}-64}\]             \[\Rightarrow \,\] \[\sqrt{{{R}^{2}}-16}=4+\sqrt{{{R}^{2}}-64}\]          \[\Rightarrow \,\] \[{{R}^{2}}-16=16+{{R}^{2}}-64+8\sqrt{{{R}^{2}}-64}\]             \[\Rightarrow \,\] \[32=8\sqrt{{{R}^{2}}-64}\]             \[\Rightarrow \,\] \[{{R}^{2}}-64=16\]             \[\Rightarrow \,\] \[{{R}^{2}}=80\]             \[\therefore \]      \[R=4\sqrt{5}\]