Question : In $\Delta ABC,\angle BAC=90^{\circ}$ and D is the mid-point of BC. Then which of the following relations is true?
Option 1: $AD=BD=CD$
Option 2: $AD=BD=2CD$
Option 3: $AD=2BD=CD$
Option 4: $2AD=BD=CD$
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Correct Answer: $AD=BD=CD$
Solution :
Given: $\angle BAC=90^{\circ}$ and D is mid-point of BC
BC would have been the diameter of a circle passing through A, B, and C.
So, AD, BD, and CD will be equal to the radius of the circle
⇒ $AD = CD = BD$
Hence, the correct answer is $AD = BD = CD$.
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