NCERT Class 10 Mathematics

11 11.1 Introduction In Class IX, you have done certain constructions using a straight edge (ruler) and a compass, e.g., bisecti ...

CONSTRUCTIONS 217 Let us see how this method gives us the required division. Since A 3 C is parallel to A 5 B, therefore, 3 35 A ...

218 MATHEMATICS Example 1 : Construct a triangle similar to a given triangle ABC with its sides equal to 3 4 of the correspondin ...

CONSTRUCTIONS 219 Solution : Given a triangle ABC, we are required to construct a triangle whose sides are 5 3 of the correspond ...

220 MATHEMATICS Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2 3 of the ...

CONSTRUCTIONS 221 Steps of Construction: Join PO and bisect it. Let M be the mid- point of PO. Taking M as centre and MO as ...

222 MATHEMATICS Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and B = 90°. BD is the perpendicular from B on AC. T ...

12 12.1 Introduction You are already familiar with some methods of finding perimeters and areas of simple plane figures such as ...

224 MATHEMATICS 12.2Perimeter and Area of a Circle — A Review Recall that the distance covered by travelling once around a circl ...

AREAS RELATED TO CIRCLES 225 You can see that the shape in Fig. 12.2 (ii) is nearly a rectangle of length 1 2 2 ✁r and breadth ...

226 MATHEMATICS Fig. 12.5 The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in ...

AREAS RELATED TO CIRCLES 227 In a way, we can consider this circular region to be a sector forming an angle of 360° (i.e., of de ...

228 MATHEMATICS Let us now take some examples to understand these concepts (or results). Example 2 : Find the area of the sector ...

AREAS RELATED TO CIRCLES 229 Solution : Area of the segment AYB = Area of sector OAYB – Area of OAB (1) Now, area of the sector ...

230 MATHEMATICS EXERCISE 12.2 Unless stated otherwise, use = 22 7. Find the area of a sector of a circle with radius 6 cm if a ...

AREAS RELATED TO CIRCLES 231 An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat c ...

232 MATHEMATICS Solution : Area of the square lawn ABCD = 56 × 56 m^2 (1) Let OA = OB = x metres So, x^2 + x^2 =56^2 or, 2 x^2 = ...

AREAS RELATED TO CIRCLES 233 Alternative Solution : Total area = Area of sector OAB + Area of sector ODC + Area of OAD + Area o ...

234 MATHEMATICS Example 6 : Find the area of the shaded design in Fig. 12.17, where ABCD is a square of side 10 cm and semicircl ...

AREAS RELATED TO CIRCLES 235 Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with cent ...