Class 10 Math: Areas Related to Circles Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 10 Areas Related to Circles to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (HARD)

Case Study-2 The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using • Four clear glass panels, trapezium in shape, all the same size • One tinted glass panel, half a regular octagon in shape (i) Find the mid-point of the segment joining the points J (6, 17) and I (9, 16). (1) (ii) Find the distance between the points A and S. (1) (iii) Find the co-ordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. (2) OR (iii) If a point (x,y) is equidistant from the Q(9,8) and S(17,8),then find the relation between x and y. (2)

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: (i) Mid-point of JI = 6 9 17 16 15 33, ,2 2 2 2 + +( ) ( ) =( ) ( )( ) ( ) (ii) Distance between A and S = 16 boxes. (iii) Coordinates of A and B are (1, 8) and (5, 10) respectively. Coordinates of point dividing AB in the ratio 1 : 3 internally are: 1 5 3 1 1 10 3 8,1 3 1 3x y × + × × + ×= = + + 8 342, 8.54 4x y⇒ = = = = Co-ordinates of required points be (2, 8.5) OR (iii) Let P (x,y) is equidistant from the Q(9,8) and S(17,8) then we have PQ = PS ⇒ PQ2 = PS2 ⇒ (x - 9)2 + (y - 8)2 = (x - 17)2 + (y - 8)2 ⇒ (x - 9)2 = (x - 17)2 ⇒ x2 - 18x + 81 = x2 - 34x + 289 ⇒ 34x - 18x + 81 - 289 = 0 ⇒ 16x - 208 = 0 ⇒ x - 13 = 0

Question 2 (EASY)

Assertion (A): The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally. Reason (R): Given three points, i.e. A, B, C form an equilateral triangle, then AB = BC = AC.
  • Option 1: Option A
  • Option 2: Option B
  • Option 3: Option C
  • Option 4: Option D

Solution Explanation & Steps: (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) SECTION - B Questions 21 to 25 carry 2 marks each.

Question 3 (EASY)

The ratio in which the line segment joining the points P(-3, 10) and Q(6, -8) is divided by O(-1, 6) is:
  • Option 1: 1:3
  • Option 2: 3:4
  • Option 3: 2:7
  • Option 4: 2:5

Solution Explanation & Steps: (c) 2:7 Let k :1 be the ratio in which the line segment joining P( -3, 10) and Q(6, -8) is divided by point O(- 1, 6). By the section formula, we have -1 = ( 6k - 3)/(k + 1) ⇒ -k - 1 = 6k - 3 ⇒ 7k = 2 ⇒ k = 2/7 Hence, the required ratio is 2:

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 10 Math Resource Hub for Areas Related to Circles: • 🧮 Interactive Solver: Solve Areas Related to Circles Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Areas Related to Circles Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Areas Related to Circles PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Areas Related to Circles Key Equations - Complete revision references. • 🔄 Next Topic Guide: Surface Areas and Volumes Study Notes • 🎓 Syllabus Overview: Class 10 Mathematics Portal - Access all chapter guides.
Back to Blog PortalGo to Homepage