Question : If $\mathrm{D}$ is the midpoint of $\mathrm{BC}$ in $\triangle \mathrm{ABC}$ and $\angle A=90^{\circ}$, then $AD=$ ______.
Option 1: $\frac{\mathrm{BC}}{4}$
Option 2: $2 \mathrm{BC}$
Option 3: $\frac{\mathrm{BC}}{2}$
Option 4: $\mathrm{BC}$
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Correct Answer: $\frac{\mathrm{BC}}{2}$
Solution :
Given: In $\triangle \mathrm{ABC}$, the midpoint of $\mathrm{BC}$ is $\mathrm{D}$ and $\angle A=90^{\circ}$.
AD is the median to the BC.
We know that the median to the hypotenuse of a right-angled triangle is half of the hypotenuse.
$AD = \frac{1}{2} BC$
Hence, the correct answer is $\frac{\mathrm{BC}}{2}$.
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