Question : In $\triangle$ABC, if the median AD = $\frac{1}{2}$BC, then $\angle$BAC is equal to:
Option 1: 90°
Option 2: 45°
Option 3: 60°
Option 4: 75°
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Correct Answer: 90°
Solution : Given: Since AD is the median of △ABC, BD = CD = $\frac{1}{2}$BC $\therefore$ AD = BD = CD Thus A, B, and C are in equal distance from point D. That means D is the circumcentre of △ ABC. Also, in a right triangle, the circumcentre lies on the midpoint of the hypotenuse. So, $\angle$BAC is 90°. Hence, the correct answer is 90°.
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