Question

Two congruent circles have centres P and P'. Arc $AXB$ subtends an angle of ${60}^{\circ }$ at the centre P and arc A'YB' subtends an angle of ${20}^{\circ }$ at the centre P'. Then the ratio of arcs $AXB$ and $A^{\prime }Y{B}^{\prime }$ is ?

• A.
  $2:1$
• B.
  $1:2$
• C.
  $3:1$
• D.
  $1:3$

Answer 1

The correct option is C

$3:1$
If 'r' is the radius of circle
we know, length of arc $=\frac{\theta }{{360}^{\circ }}\times 2\pi r$

Given, both circles are congruent.
$\therefore$ Radius of both circles is same.

Hence, ratio of arcs is:

$\frac{AXB}{A^{\prime }Y{B}^{\prime }}=\frac{(\frac{{60}^{\circ }}{{360}^{\circ }}\times 2\pi r)}{(\frac{{20}^{\circ }}{{360}^{\circ }}\times 2\pi r)}=\frac{3}{1}$

$=3:1$

Hence, the correct option is (c).