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Question


In ΔABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then AD.DC =


A

BD2

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B

BE.BC

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C

AB.BC

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D

BD.DC

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Solution

The correct options are
A

BD2


B

BE.BC


In ΔABD & ΔBDCADB=BDC=90A=DBC ( Since in ΔBDC,DBC=90C=A
In ΔABCA=90C),ΔADBΔBDC by AA-similarity
ADDB=BDDC=ABBCBD2=AD.DC
Similarly ΔBDCΔBEDDBC=DBE (Common angle)BDC=DEB = 90BDBE=DCED=BCBDBD2=BE.BCBD2=AD.DC=BE.BC


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