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Question


In ABC, 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 ABD and BDC
ADB=BDC=90
A=DBC (Since in BDC,DBC=90C=A
and in ABCA=90C)
Therefore, ADBBDC by AA similarity
ADDB=BDDC=ABBC
BD2=AD.DC

DBC=DBE (Common angle)
BDC=DEB=90
Similarly BDCBED

BDBE=DCED=BCBD
BD2=BE×BCBD2=AD×DC=BE×BC


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