question_answer

If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is

A) 6 cm

B) 7 cm

C) 10 cm

D) 8 cm

Correct Answer: D

Solution :

[d] Let the chord of greater circle which touches the smaller. Circle be AB at M. Given OM = 3 cm, OA = 5 cm In \[\Delta AMO,\]\[{{(OA)}^{2}}={{(AM)}^{2}}+{{(OM)}^{2}}\] \[\Rightarrow \]   \[{{(5)}^{2}}={{(AM)}^{2}}+{{(3)}^{2}}\] \[\Rightarrow \]   \[25={{(AM)}^{2}}+9\] \[\Rightarrow \]   \[{{(AM)}^{2}}=16\]\[\Rightarrow \]\[AM=4\] \[\Rightarrow \]   \[AB=2\times AM\] \[\Rightarrow \]   \[AB=2\times 4\,cm\]\[\Rightarrow \]\[AB=8\,cm\] Hence, the required length of chord is 8 cm.