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ICSE Class 9 Answered

In an isoceles triangle  ABC, AB=AC and D is a point BC produced. Prove that 

AD^2=AC^2 + BD * CD

Asked by bsap6777 | 28 Aug, 2018, 09:50: PM
Expert Answer
 
begin mathsize 16px style increment ACB space is space isosceles space triangle.
AO perpendicular BC space and space BO equals CO
In space increment AOD comma
AO squared plus OD squared equals AD squared........ left parenthesis straight i right parenthesis
In space increment AOB comma
AO squared plus OB squared equals AB squared........ left parenthesis ii right parenthesis
Subtract space left parenthesis ii right parenthesis space from space left parenthesis straight i right parenthesis
AD squared minus AB squared equals OD squared minus BO squared
AD squared minus AB squared equals left parenthesis OD plus BO right parenthesis left parenthesis OD minus BO right parenthesis
AD squared minus AB squared equals BD left parenthesis OD minus OC right parenthesis
AD squared minus AB squared equals BD cross times CD
AD squared equals equals AB squared plus BD cross times CD end style
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