question_answer

Two concentric circles having common centre 'O' and chord AB of the outer circle intersect the inner circle at points C and D. If distance of chord from the centre is 3 cm, outer radius is 13 cm and inner  radius is 7 cm, then length of AC (in cm) is

A) \[8\sqrt{10}\]

B) \[6\sqrt{10}\]

C) \[4\sqrt{10}\]

D) \[2\sqrt{10}\]

Correct Answer: D

Solution :

[d] From figure, In \[\Delta OCM,\]\[C{{M}^{2}}={{7}^{2}}-{{3}^{2}}=40\] \[\therefore \]      \[CM=2\sqrt{10}\,cm\] In \[\Delta AOM\] \[AM=\sqrt{{{13}^{2}}-{{3}^{2}}}=4\sqrt{10}\] Now, \[AC=AM-CM=2\sqrt{10}\,cm\]