Can someone please explain me the solution for this problem. The correct answer is **B**

Thanks in advance.

When the angle is 45 it means that the BD and OD are equal since Tan 45 = 1 = BD/OD = Tan BOD

But when angle AOB is 44 -> angle BOD is 46 and we know that Tan 46 > Tan 44. So BD/OD when BOD is 46 is greater than 1. Which implies that BD is greater than OD.

If you want a logical explanation rather than a trigonometric one …Let us assume B as a point moving from C to A along the circumference of the circle. And when B is close to (or on) C then BD is close to Zero and as it moves towards A value of BD keeps increasing as OD decreases. BD will be equal to OD when the angle is 45. So when the angle BOD is greater than 45 it means that BD is greater than OD.

Hope that answers your question.

As mentioned AOC = 90° which means BOD will be 90-44 = 46°, as BDO is 90° we can get OBD by 180-90-46 = 44°. So now we have ∠BOD = 46°, ∠BDO = 90° and ∠OBD = 44°. As per triangle properties, the angle of a vertex is directly proportional to the length of its opposite side.

As we know all 3 angles 90° > 46° > 44° ~ OB > BD > OD