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Prove that the mid-point of the hypoten...

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

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`Here/_CAB=90^(@)` let D be the mid -point of hypotenuse,
We have
BD=DC
AB=AD+DB
Ac=AD+DC=AD+BD…(i)

since ,`angleBAC=90^(@)`
`ABbotAC`
`(AD+DB).(AD+BD)=O`
`(AD-BD).(AD+BD)=O`
`AD^(2)-BD^(2)=O`
`thereforeAD=BDalso,BD=DC`
`"thereforeD is mid-pointof BC".`
` thus ,|AD|=|BD|=|DC|.`
Hence ,its proved that the mid -point of the hypotenuse of right angled triangle is equidistant from its vertices.
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