Formative Assessment
Project Work
Preliminary Information
Class: 10th
Subject: Mathematics
Name of the unit: Secants and Tangents to a circle
No. of the Project:
Medium: English
Allotment of work: Group work
1) Collect the information
2) Record the data
3) Analyse the data
4) Presentation
Detailed information of the Project
Title of the Project: Find the area of a segment.
Objectives of the Project: To find the area inscribed by four equal circles.
Material used: White board, Scissors, Colour papers, Compass box.
Procedure: Observe the following figure. How to find the area of the shaded Part PQRS
Collection of Data/Preparation:
Prepare 4 equal radii circles form the colour papers. Let the radius of each circle be 'r' units. Now paste these four circles on white board as shown in the following figure.
A, B, C, D are the centres of four circles. We have to find the shaded part area inscribed by the four circles.
To find the area, join the centres of circles as shown in the figure. Now we get a square ABCD whose side length is 2r units.
Analysis:
From the figure we have four sectors I, II, III and IV. These sectors are the quarter circles. Therefore centre angle of each sector is 90°.
Area of shaded region = Area of square ABCD − Area of four sectors
Area of four sectors = 4 × 
× Πr2 = Πr2 = Area of circle.
∴ Area of shaded region PQRS = Area of square ABCD − Area of one circle
Now area of square ABCD = Side × Side
= 2r × 2r
= 4r2
Area of one circle = Πr2 (... radius = r)
∴ Area of shaded region PQRS = 4r2 − Πr2
= (4 − Π)r2 sq.cm
Conclusion: From this project, we conclude that we can find the area of segment.
Experiences of the students:
i) We enjoyed while doing this project.
ii) We got a clear idea about finding the area of a segment.
Doubts and Questions:
How can we measure the radius of shaded region sectors?
Acknowledgements:
We convey our sincere thanks to our guide teacher.
Reference books/ Resources:
i) APSCERT X Class Maths test book
ii) Mathematics Projects by N.M. Rao
iii) NCERT X Class Maths text book
Signatures of the students
I. Answer the following questions. 2 × 4 = 8
1. A Chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding.
i) Minor Segment ii) Major Segment
2. Draw a circle of radius 6 cm, from a point 10 cm, away from its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythagoras theorem.
II. Answer the following questions. 3 × 2 = 6
3. Prove that the tangents at the extremities of any chord make equal angles with the chord.
4. In two concentric circles, a chord of length 24 cm of larger circle be comes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.
5. Prove that the centre of a circle lies on the bisector of the angle between two tangents drawn from a point outside it.
III. Answer the following questions. 3 × 1 = 3
6. Calculate the length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm.
7. The radius of a circle is 6 cm. Find the area of the square inscribed in the circle.
8. Draw a diagram to the following three circles are drawn such that their centres are the vertices of a triangle and each circle touches the other two.
IV. Choose the correct option and put the Capital Letter in given brackets. 6 × 1/2 = 3
9. From an external point P, a tangent of length 4 cm is drawn to a circle of radius 3 cm, then the distance between the centre and P is
A) 3 cm B) 4 cm C) 5 cm D) 8 cm ( )
10. The area of sector, whose radius is 
cm with central angle 90° is ......... cm ( )
11. Radius of a circle is 4 cm. The distance between two parallel tangents to the circle is ......cm ( )
A) 4 B) 8 C) 2 D) 16
12. The number of tangents that can be drawn to a circle are ( )
A) 2 B) 1 C) 0 D) Infinite
13. A segment is a region, bounded by the arc and ( )
A) a sector B) a diameter C) a chord D) a radius
14. The number of secants pass through a point on the circle are ( )
A) 0 B) 1 C) 2 D) Infinite
