Q. 174.1( 8 Votes )

# In the given figure, D is the midpoint of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that

(i) b^{2} = p^{2} + ax + a^{2}/4

(ii) c^{2} = p^{2} -ax + a^{2}/4

(iii) (b^{2} + c^{2}) = 2p^{2} + 1/2 a^{2}

(iv) (b^{2} - c^{2}) = 2ax

Answer :

(i) ΔAEC and ΔAED are right triangles.

Applying Pythagoras theorem we get,

AC^{2} = EC^{2} + AE^{2}

And AD^{2} = ED^{2} + AE^{2}

….(i)

And p^{2} = h^{2} + x^{2} ….(ii)

Putting (ii) in (i),

…..(iii)

Hence, proved.

(ii) ΔAEB is a right triangle.

Applying Pythagoras theorem we get,

AB^{2} = EB^{2} + AE^{2}

….(iv)

Putting (ii) in (iv ),

…..(v)

Hence, proved.

(iii) Adding (iii) and (v),

Hence, proved.

(iv) Subtracting (iii) and (v),

Hence, proved.

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

A Peep into Pythagoras Theorem43 mins

R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class

NCERT | Strong Your Basics of Triangles39 mins

RD Sharma | Imp. Qs From Triangles41 mins

Quiz | Criterion of Similarity of Triangle45 mins

How to Ace Maths in NTSE 2020?36 mins

Know About Important Proofs in Triangles33 mins

Master BPT or Thales Theorem39 mins

Champ Quiz | Thales Theorem49 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation