एक त्रिभुज जिसके शीर्ष बिन्दु \(A (-2,3), B (1,9)\) तथा \(C(3,8)\) हैं, पर विचार कीजिए। यदि एक रेखा \(L\), जो त्रिभुज \(ABC\) के परिकेन्द्र से होकर जाती है रेखा \(BC\) को समद्विभाजित करती है तथा \(y\)-अक्ष को बिन्दु \(\left(0, \frac{\alpha}{2}\right)\) पर काटती है, तो वास्तविक संख्या \(\alpha\) का मान है .......... |

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.