Multiple choice

Let ABC be a tringle in which the line joining the circumcentre and incentre is parallel to the base of the triangle, then answer the given question: Then range of $ \angle\ A$ is,

  1. $ \left[ \dfrac { \pi }{ 6 } ,\dfrac { \pi }{ 3 } \right]$
  2. $ \left[ \dfrac { \pi }{ 3 } ,\dfrac { \pi }{ 2 } \right]$
  3. $ \left[ \dfrac { \pi }{ 6 } ,\dfrac { 2\pi }{ 3 } \right] -\left\{ \dfrac { \pi }{ 2 } \right\}$
  4. $ \left\{ 0.\dfrac { \pi }{ 2 } \right\}$
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A Correct answer
Explanation

For the line joining the circumcenter and incenter to be parallel to the base, the triangle must satisfy specific geometric properties related to the Euler line and triangle centers. This is a known result in triangle geometry.

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