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First let us take a Right angled triangle DAB, Right angled at A.
Given:ABD is triangle, right angled at A.
Construction: Draw perpendicular from A to BD
TO Prove : AB^2/AD^2=BC/CD
In triangle DAC and ABD
DC/DA = DA/DB
AD^2= DC.DB. ......eq 1
In triangle DAC and triangle ABC
AD/AB = AB/DB
AB^2= AD. DB. ......eq 2
from eq 1 and 2
DC.BD = CD.BD
DC = CD
then,
CD = BC, because the perpendicular lines cuts the Hypotenuse in two equal parts.
therefore, AB^2/AD^2 = BC/CD.
Hence Proved.
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Abhinandhan:
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