SSC
Quantitative Aptitude
Circular Measurement
Question Bank
Circle and Its Properties (I)
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, \[AC=AM-CM=2\sqrt{10}\,cm\]