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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]
ADDB=BDDC=ABBCBD2=AD.DC
Similarly, BDCBED
DBC=DBE  [Common angle]
BDC=DEB  [90]
BDBE=DCED=BCBDBD2=BE.BC
BD2=AD.DC=BE.BC


Mathematics

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