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 \[AC=2AB=2\times 8\,\,\text{inc}\,=16\,\,\text{inch}\]You need to login to perform this action.
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