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Question

ABC is a triangle, right angled at B. BD is a perpendicular to AC as shown. Which of the following is true?



A

AB×BC=AD×DC

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B

AD2 + CD2 = BD2 +  AB2

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C

AB2 + CD2 = BC2 +  AD2

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D
None of the above
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Solution

The correct option is B

AB2 + CD2 = BC2 +  AD2


Since ΔADB and ΔDBC are right triangles, using Pythagoras theorem, we can write:

AB2=AD2+BD2  ...(1)

BC2=CD2+BD2  ...(2)

Subracting (2) from (1), we get,

AB2=AD2+BD2BC2=CD2+BD2()        ()     ()–––––––––––––––––––AB2BC2=AD2CD2

Rearranging, we get,
AB2+CD2=AD2+BC2


Mathematics

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