A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then Options: A . &nbspAB2 + CD2 = AD2 + BC2 B . &nbspCD2 + BD2 = 2AD2 C . &nbspAB2 + AC2 = 2AD2 D . &nbspAB2 = AD2 + BC2

A point D is taken on the side BC of a right-angled triangle ABC, where AB is hy

Question

A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

Options:

A . AB2 + CD2 = AD2 + BC2

B . CD2 + BD2 = 2AD2

C . AB2 + AC2 = 2AD2

D . AB2 = AD2 + BC2

Answer: Option A
According to question,
In ΔABC
AB2 = AC2 + BC2 . . . . . . . (i)
ΔACD
AD2 = AC2 + CD2
AC2 = AD2 - CD2 . . . . . . . (ii)
Put the value of AC2 in equation (i)
AB2 = AD2 - CD2 + BC2
AB2 + CD2 = AD2 + BC2

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