Question

52pqr(2pqr + p2q + pq2 + q2r + qr2 + p2r + pr2)÷ 104pq(q +r)(r + p)

Answer 1

Answer:

Given, In ΔPQR

Refer image,

PR

2

−PQ

2

=QR

2

and QM⊥PR

To prove: MQ

2

=MP×MR

Proof: In ΔPQR

PR

2

−PQ

2

=QR

2

[Given]

PR

2

=PQ

2

+QR

2

∴ΔPQR=90

0

[By conv, of Pythagoras theorem]

Now in ΔQMP and ΔQMR

∠1=∠2=90

0

(∵QM⊥PR)

∠P=90

0

−∠R

∠3=90

0

−∠R

∠P=∠3

∴ΔQMP∼ΔRMQ (By AA similarity criterion)

QR

PQ

=

QM

PM

=

RM

QM

=QM

2

=PM×RM

Hence proved.

solution