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Question

ABC is a triangle right-angled at B and D is a point on BC produced (BD>BC), such that BD=2DC. Which one of the following is correct?

A
AC2=AD23CD2
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B
AC2=AD22CD2
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C
AC2=AD24CD2
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D
AC2=AD25CD2
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Solution

The correct option is A AC2=AD23CD2
Given, BD=2DC
BC+CD=2DCBC=DC
In ABC, applying pythagoras theorem
AC2=AB2+BC2 ....(i)
In ABD, appying pythagoras theorem
AD2=AB2+BD2 .....(ii)
Subtracting equations (i) and (ii), we have
AC2AD2=BC2BD2
AC2AD2=CD2(2CD)2
=CD24CD2
=3CD2
AC2=AD23CD2

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