CBSE Class 10 Mathematics Standard 2023: question 18
Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q18 · 1 mark · MCQTriangles
In the given figure, . If cm, cm and cm, then the length of is :
- (A) cm
- (B) cm
- (C) cm
- (D) cm
Figure in the paper: AB and PQ are two parallel segments, AB = 6 cm (A at bottom left, B at top) and PQ = 2 cm (P lower, Q upper right). Lines AQ and BP intersect at O. BO = 3 cm is marked along BP, and OP is the unknown segment. See it in the official paper.
Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.
Hints
Open one hint at a time and try again before the next.
Hint 1
Look for two similar triangles meeting at O.
Hint 2
Corresponding sides are proportional: AB ↔ PQ, OB ↔ OP.
Step-by-step solution
Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.
(vertically opposite angles, alternate angles as ).
- 1 mark
cm.
Answer: 1 cm, option (D)
Where the marks are
- Similarity ratio gives OP = 1 cm (1 mark)
Revise the chapter
- Chapter: Triangles (notes, formulas, where marks are lost and every past question)
- Topic: Basic Proportionality Theorem (Thales Theorem)
More questions from Triangles
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The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.