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प्रश्न
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.
उत्तर
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)
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