#### 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.

#### Solution

In Δ POQ, AB || PQ

:.`(OA)/(AP) = (OB)/(BQ) ` (basic proportionality theorem) (i)

In ΔPOR, AC||PR

`:.(OA)/(AP) = (OC)/(CR)` (By basic proportionality theorem) (ii)

From i and ii, we obtain

`(OB)/(BQ) = (OC)/(CR)`

`:. BC || OQ` (By Converse of basic proportionality theorem)

Is there an error in this question or solution?

Solution 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. Concept: Similarity of Triangles.