Maths · Geometry · chapter 10 of 14
Class 10 Maths Chapter 10: Circles case study question with answers
One case-based question of the kind the board asks in Section E: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A park in Jaipur has a circular flower bed with centre O and radius 28 m. From the park gate G, two straight paths GA and GB are laid so that each just touches the edge of the bed, at A and at B, as in the figure. The gate is 53 m from the centre of the bed. The gardener wants to know the lengths of the paths and the angles they make, so that he can order the paving stones and edge the paths with a hedge.
Part 1 · 1 mark
The angle between the radius OA and the path GA is
Show answer
Answer: (c) 90°
The path touches the bed at A, so it is a tangent there, and the tangent is perpendicular to the radius OA.
Part 2 · 1 mark
The length of the path GA is
Show answer
Answer: (b) 45 m
GA = √(53² − 28²) = √2025 = 45 m, with the right angle at A.
Part 3 · 2 marks
If ∠AOB is four times ∠AGB, find ∠AGB and ∠AOB.
Answer and marking scheme
∠AGB + ∠AOB = 180°, as ∠OAG = ∠OBG = 90° in quadrilateral OAGB. So ∠AGB + 4∠AGB = 180°: ∠AGB = 36° and ∠AOB = 144°.
- ∠AGB + ∠AOB = 180° (1)
- ∠AGB = 36°, ∠AOB = 144° (1)
Or
Find the total length of hedge needed along both paths and the two radii OA and OB, that is, the perimeter of OAGB.
Answer and marking scheme
GB = GA = 45 m (tangents from G). Perimeter = 28 + 45 + 45 + 28 = 146 m.
- GB = GA = 45 m (1)
- perimeter = 146 m (1)
← Chapter 9: Some Applications of TrigonometryChapter 11: Areas Related to Circles →