Two variable chords AB and BC of a circle ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2$ are such that AB = BC = a. M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle.

$\mathrm{\angle }\mathrm{OAB}$ is 

• A

  30°

• B

  60°

• C

  45°

• D

  15°

The angle between the tangents at A and C is

• A

  90°

• B

  120°

• C

  60°

• D

  150°

The locus of the point of intersection of tangents at A and C is 

• A

  ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2$

• B

  ${\mathrm{x}}^2+{\mathrm{y}}^2=2{\mathrm{a}}^2$

• C

  ${\mathrm{x}}^2+{\mathrm{y}}^2=4{\mathrm{a}}^2$

• D

  ${\mathrm{x}}^2+{\mathrm{y}}^2=8{\mathrm{a}}^2$

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