Q1. [1] § 6.1 Introduction § 6.3 Similarity of Triangles § 6.5 Summary
In the given figure, $AB \parallel PQ$. If $AB = 6$ cm, $PQ = 2$ cm and $OB = 3$ cm, then the length of $OP$ is:
- (a) $9$ cm
- (b) $3$ cm
- (c) $4$ cm
- (d) $1$ cm
Previously asked in CBSE board exam
2023 30/2/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer
(d) 1 cm
In △OAB and △OPQ, AB ∥ PQ, so △OAB ~ △OPQ (AA similarity).
$$\frac{OP}{OB} = \frac{PQ}{AB} \implies \frac{OP}{3} = \frac{2}{6} = \frac{1}{3} \implies OP = 1 \text{ cm}$$
Explanation
Since AB ∥ PQ, the two triangles OAB and OPQ are equiangular (AA criterion). Use the ratio of corresponding sides: PQ/AB = 2/6 = 1/3. Apply this ratio to OB = 3 cm to get OP = 1 cm. A common mistake is using OB/OP = AB/PQ instead of the correct correspondence OP/OB = PQ/AB.
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