Q. 224.5( 4 Votes )

# In Δ ABC, ∠ B = 90° and D is the mid-point of BC. Prove that AC2 = AD2 + 3CD2.

Answer :

Given: In Δ ABC, ∠B = 90° and D is the mid-point of BC.
To Prove: AC2 = AD2 + 3CD2
Proof:
In Δ ABD,
AD2 = AB2 + BD2
AB2 = AD2 - BD2 ……………..(i)
In Δ ABC,
AC2 = AB2 + BC2
AB2 = AC2 - BC2 ……………..(ii)
Equating (i) and (ii)
AD2 - BD2 = AC2 - BC2
AD2 - BD2 = AC2 – (BD + DC)2
AD2 - BD2 = AC2 – BD2 - DC2 – 2BD × DC
AD2 = AC2 - DC2 – 2DC2 (DC = BD)
AD2 = AC2 - 3DC2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Champ Quiz | Thales Theorem49 mins
Quiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?36 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 mins
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
view all courses