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Question

ABC is a right angled triangle, right angled at B. BD is a perpendicular 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 these

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Solution

The correct option is C

AB2 + CD2 = BC2 + AD2


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

AB2 = AD2 + BD2 ------ (1)

BC2= BD2 + DC2 ------ (2)

Subtracting (1) and (2) and cancelling out the common terms ( DB2), we get, AB2BC2 = AD2DC2. Rearranging, we see that option (c) is correct, AB2 + CD2 = AD2 + BC2


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