Skip to content

A, B and C are points on… (Class 10 Maths Basic 2023, Q25)

questionbuddy.in/q/cbse-10-maths-2023-430-4-1-q25-adjoining-points-respectively-such

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 25

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerTriangles

In the adjoining figure, A, B and C are points on OP, OQ and OR respectively such that and . Show that .

Figure in the paper: A triangle PQR with P at the top, Q at bottom-left and R at bottom-right. O is a point inside the triangle, and P, O, A lie on a line from P, with A between P and O. Lines OP, OQ and OR are drawn from O. A lies on OP, B lies on OQ and C lies on OR. AB is drawn parallel to PQ and AC is drawn parallel to PR. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Use the Basic Proportionality Theorem in triangles POQ and POR.

Hint 2

Both ratios share ; then use the converse of BPT in △QOR.

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.

  1. In , , so ...(i) [Basic Proportionality (Thales) Theorem]

    ½ mark

  2. In , , so ...(ii) [BPT]

    ½ mark

  3. From (i) and (ii):

    ½ mark

  4. Hence in , B and C divide OQ and OR in the same ratio, so [converse of BPT].

    ½ mark

Answer: BC ∥ QR (proved)

Where the marks are

  • Applies BPT in △POQ (½ mark)
  • Applies BPT in △POR (½ mark)
  • Equates the ratios (½ mark)
  • Concludes BC ∥ QR by converse of BPT (½ mark)

Revise the chapter

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 430/4/1 (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.