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Question

In a right triangle ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. Which of the following statements are true?


A

ADBABC

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B

ADBBDC

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C

ABCBDC

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D

None of these

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Solution

The correct options are
A

ADBABC


B

ADBBDC


C

ABCBDC



Consider ABD and ABC,
BAD=BAC [common angle]
ADB=ABC [90]
By AA similarity, ADBABC
Consider BDC and ABC,
DCB=BCA [common angle]
BDC=ABC [90]
By AA similarity, BDCABC
Since, ADBABC and BDCABC,

so, BDCADB.
Hence, all three options are correct.


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