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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