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प्रश्न
In a right ∆ABC right-angled at C, if D is the mid-point of BC, prove that BC2 = 4(AD2 − AC2).
उत्तर
It is given that ∆ABC is a right-angled at C and D is the mid-point of BC.
In the right angled triangle ADC, we will use Pythagoras theorem,
AD2 = DC2 + AC2 ..........(1)
Since D is the midpoint of BC, we have
`"DC"/="BC"/2`
Substituting `"DC"/="BC"/2` in equation (1), we get
`"AD"^2=("BC"/2)^2+"AC"^2`
`"AD"^2="BC"^2/4+"AC"^2`
4AD2 = BC2 + 4AC2
BC2 = 4AD2 - 4AC2
BC2 = 4(AD2 - AC2)
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