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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 ABC, A=90C)

Therefore, ADBBDC  (by AA similarity criterion)

ADDB=BDDC=ABBC

BD2=AD.DC

Also, in BDC and BED ,

DBC=DBE  [Common angle]

BDC=BED  [90]

Thus, by AA similarity criterion, we have BDCBED 

BDBE=DCED=BCBD

BD2=BE.BC

BD2=AD.DC=BE.BC


Mathematics

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