Answer :

Given: A is right angle.


CD is median.



To prove: BC2 = CD2 + 3AD2


Proof:


We know that median divides the side into two halves.


So,


AB = 2AD = 2BD ………… (1)


By applying Pythagoras theorem in ΔADC, we have,


CD2 = AD2 + AC2


AC2 = CD2 - AD2 ……… (2)


By applying Pythagoras theorem in ΔABC, we have,


BC2 = AB2 + AC2 ………… (3)


Substituting from eqn. (1) and (2) into (3) gives,


BC2 = (2AD)2 + (CD2 - AD2)


BC2 = 4AD2 + CD2 - AD2


BC2 = CD2 + 3AD2


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

A person goes 24mWest Bengal Board - Mathematics

Two rods of 13m. West Bengal Board - Mathematics

In ΔABC, if AB = West Bengal Board - Mathematics

If the lengths ofWest Bengal Board - Mathematics

In the adjoining West Bengal Board - Mathematics

I have drawn a trWest Bengal Board - Mathematics

Let us fill in blWest Bengal Board - Mathematics

In ΔRST, <span laWest Bengal Board - Mathematics

If the followingsWest Bengal Board - Mathematics

The point O is siWest Bengal Board - Mathematics