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

In Δ POQ, AB || PQ

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

In ∆OPR, 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)