In the adjoining figure, A, B and C are points on OP, OQ and OR
Triangles (10)In the adjoining 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
$$ \text{In } \triangle POQ, AB \parallel PQ $$
By Thales Theorem,
$$ \Rightarrow \frac{OA}{AP} = \frac{OB}{BQ} $$
$$ \text{In } \triangle POR, AC \parallel PR $$
$$ \Rightarrow \frac{OA}{AP} = \frac{OC}{CR} $$
From (i) and (ii),
$$ \frac{OB}{BQ} = \frac{OC}{CR} $$
$$ \therefore \triangle QOR, BC \parallel QR $$
(By converse of Thales theorem)
Exam Year:
2023
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