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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 and ΔBDCADB=BDC=90A=DBC (Since in ΔBDC,DBC=90C=A and In ΔABCA=90C)Therefore,ΔADBΔBDC by AA similarityADDB=BDDC=ABBCBD2=AD.DCSimilarly ΔBDCΔBEDDBC=DBE  (Common angle)BDC=DEB = 90BDBE=DCED=BCBDBD2=BE.BCBD2=AD.DC=BE.BC

Mathematics

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