In a right ΔABC right-angled at C if D is the mid-point

In a right ΔABC right-angled at C if D is the mid-point
|

In a right ΔABC right-angled at C, if D is the mid-point of BC, prove that BC2=4(AD2−AC2).

Please scroll down to see the correct answer and solution guide.

Right Answer is:

SOLUTION


In triangleACD by Pythagoras theorem,
ADblank squared=ACblank squared+CDblank squared                    ------------ (i)

In triangleACB by Pythagoras theorem,
ABblank squared= ACblank squared+BCblank squared                  --------------(ii)

AD is median, Hence CD = BD = fraction numerator B C over denominator 2 end fraction
In eqn (i)
CDblank squared=ADblank squared - ACblank squared 
left parenthesis fraction numerator B C over denominator 2 end fraction right parenthesis squared= ADblank squared- ACblank squared
BCblank squared = 4 ( ADblank squared - ACblank squared)
Hence Proved

Related Questions