In the given figure, AB ∥ CD. If AB = 5 cm, CD = 2 cm and OB = 3 cm, then the length of OC is (A) 15/2 cm (B) 10/3 cm (C) 6/5 cm (D) 3/5 cm

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 9

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQTriangles

In the given figure, $A B ∥ C D$ . If $A B = 5$ cm, $C D = 2$ cm and $O B = 3$ cm, then the length of OC is

(A) $\frac{15}{2}$ cm
(B) $\frac{10}{3}$ cm
(C) $\frac{6}{5}$ cm
(D) $\frac{3}{5}$ cm

Figure in the paper: Points B (top left), A (bottom left), D (top right) and C (bottom right). Segment BC and segment AD cross at point O. AB is marked 5 cm and CD is marked 2 cm, with arrow marks showing AB parallel to CD. BO is marked 3 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

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: OB matches OC, AB matches CD.

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.

$△ A O B \sim △ D O C$ (AA: alternate angles as $A B ∥ C D$ , vertically opposite angles at O).
$\frac{O B}{O C} = \frac{A B}{C D} \Rightarrow \frac{3}{O C} = \frac{5}{2} \Rightarrow O C = \frac{6}{5}$ cm. Option (C).
1 mark

Answer: $\frac{6}{5}$ cm, option (C)

Where the marks are

Uses similarity ratio to get $O C = \frac{6}{5}$ cm (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/1/1 (Basic): every question, by section.

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.

CBSE Class 10 Mathematics Basic 2023: question 9

Hints

Step-by-step solution

Revise the chapter

More questions from Triangles