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Circles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCircles1 Mark
MCQ
The given figures show two congruent circles with centre $O$ and $O’$. Arc $AXB$ subtends an angle of $75^\circ$ at the centre and arc $A’YB’$ subtends an angle of $25^\circ $ at the centre $O’.$ Then, the ratio of arcs $AXB$ to $A ‘YB’$ is:
  • A
    It is $2 : 1$
  • ✓
    It is $3 : 1$
  • C
    It is $1 : 3$
  • D
    It is $1 : 2$
✓

Answer

Correct option: B.
It is $3 : 1$

Since, circles are congruent thus we can consider the two arcs as in the same circle. Now the length of the arcs is directly proportional the angle subtended by the arcs. Therefore the lengths of the given arcs would be same in ratio as the ratio of the given angles.
Hence the required ratio is $\frac{75}{25}=\frac{3}{1}.$

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