Question

Through A,B and C, lines RQ,PR and QP have been drawn respectively parallel to sides BC,CA and AB of triangle abc show that bc=1/2 qr

Answer 1

Refer to the attachments...

Answer 2

Given,

RQ,PR and QP are parallel to sides BC,CA and AB of triangle ABC.

To Find,

BC=1/2QR

Solution,

From the given data we know,

AR is parallel to BC

AC is parallel to RB

Therefore,

ARBC is a parallelogram,

Hence BC=AR--------(1)

Also, AQCB is a parallelogram

where, BC=AQ--------(2)

After adding (1) and (2),we get,

⇒2BC=AR+AQ

⇒2BC=QR

⇒BC=1/2QR

Hence, in ABC triangle BC=1/2QR.