Question

In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR. 
 

Answer 1

To Prove: BC || QR
Proof:

In ∆ POQ, AB || PQ  
∴\(\frac{OA}{AP}=\frac{OB}{BQ}\)............(i)

In ∆ POR, AC||PR
∴\(\frac{OA}{AP}=\frac{OC}{CR}\)...........(ii)

From (i) and (ii) we obtain,
\(\frac{OB}{BQ}=\frac{OC}{CR}\)

∴ BC || QR

(By the converse of the basic proportionality theorem)

Hence Proved