50 Views

In any triangle ABC, show that AB*AB+AC*AC=2(AD*AD+BD*BD)where D is the midpoint of BC


Arjun Sharma 6th Sep, 2018
Answer (1)
Vishakha Khandelwal 3rd Apr, 2019
Hello Arjun,



This question uses multiple properties of triangles.

The line joining one vertex of a triangle and the midpoint of the side opposite to the vertex is perpendicular to that side.

This means that AD is the height of the triangle

Now using Pythagoras theorem,

AD^2 = AB^2 + BD^2

Also AD^2 = AC^2 + DC^2

BD = DC

Adding the two equations you will get the required answer.



Hope this helps.

All the best!











Related Questions

Woxsen University B.Sc. Admis...
Apply
Build Your Own Degree - Choose any 3 out of 8 Electives | 100% Plcament track | 100+ Global Partners | 200+ Industry Interactions
Symbiosis School for Liberal ...
Apply
Admissions open for BA/BSc. Liberal Arts (Honours) & BA / BSc. Liberal Arts (Honors) with Research
UPES B.Sc Admissions 2025
Apply
Ranked #46 amongst Universities in India by NIRF | Ranked #1 in Academic Reputation in India by QS World University Rankings
Alliance University B.Sc. Adm...
Apply
Highest CTC 60.1 LPA | 800+ Recruitment Partners
Chandigarh University Admissi...
Apply
Ranked #1 Among all Private Indian Universities In QS Asia Rankings 2025 | Scholarships worth 210 CR
GMAT™ Exam
Apply
Select test center appointment | Scores valid for 5 Years | Multiple Attempts | Round 2 Closing Soon
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books