question_answer

If radii of two concentric circles are 6 inch and 10 inch, then length of each chord of one circle which is tangent to the other circle is

A)  8 inch                          

B)  16 inch        

C)  20 inch           

D)  19 inch

Correct Answer: B

Solution :

(b): Let O be the centre of two concentric circles \[{{C}_{1}}\] and \[{{C}_{2}}\], whose radii are \[{{r}_{1}}=3\,cm\]and \[{{r}_{2}}=10\text{ }cm\]. Now, we draw a chord AC which touches a circle \[{{C}_{1}}\] at B. Also, join OB, which is perpendicular to AC. \[\therefore \]      In right \[\Delta \,OAB\].             \[O{{A}^{2}}=A{{B}^{2}}+B{{O}^{2}}\]                                      (By Pythagoras theorem) \[\Rightarrow \]   \[{{10}^{2}}=A{{B}^{2}}+{{6}^{2}}\] \[\Rightarrow \]   \[A{{B}^{2}}=100-36=64\] \[\Rightarrow \] \[AB=8\] \[\therefore \]      Length of chord             \[AC=2AB=2\times 8\,\,\text{inc}\,=16\,\,\text{inch}\]