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In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Q6  In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR.
       Show that BC || QR.

      

Answers (1)
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Given : AB || PQ and AC || PR

To prove : BC || QR

 Since ,AB || PQ so we have 

\frac{OA}{AP}=\frac{OB}{BQ}.............................................1

Also, AC || PR

\frac{OA}{AP}=\frac{OC}{CR}.............................................2

 

From equation 1 and 2, we have 

\frac{OB}{BQ} = \frac{OC}{CR }

Therefore, BC || QR. (converse basic proportionality theorem)

Hence proved 

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