Chapter 12 Areas Related to Circles Ex 12.3
Chapter 12 Areas Related to Circles Ex 12.3 Question 1. Find the area of the shaded region in the given figure, if PQ = 24cm, PR = 7cm and O is the centre of the circle. Solution: Question 2. Find the area of the shaded region in the given figure, if radii of the two […]
Chapter 12 Areas Related to Circles Ex 12.2
Chapter 12 Areas Related to Circles Ex 12.2 Question 1. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. Solution: Radius of the sector (r) = 6 cm Central angle of the sector = 60° Question 2. Find the area of a quadrant of […]
Chapter 12 Areas Related to Circles Ex 12.1
Chapter 12 Areas Related to Circles Ex 12.1 Question 1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Solution:Given: radius of 1st circle (R1) = 19 cm ∴ Circumference of 1st circle = 2πR1 = […]
Chapter 11 Constructions Ex 11.2
Chapter 11 Constructions Ex 11.2 In each of the following, give the justification of the construction also: Question 1. 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. Solution: Steps of Construction: 1. Draw a circle […]
Chapter 11 Constructions Ex 11.1
Chapter 11 Constructions Ex 11.1 In each of the following, give the justification of the construction also: Question 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Solution: Steps of Construction: 1. Draw a line segment AB = 7.6 cm. 2. Draw an acute […]
Chapter 10 Circles Ex 10.2
Chapter 10 Circles Ex 10.2 Question 1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (a) 7 cm Sol. (b) 12 cm (c) 15 cm (d) 24.5 cm Solution: Question 2. […]
Chapter 10 Circles Ex 10.1
Chapter 10 Circles Ex 10.1 Question 1. How many tangents can a circle have? Solution: There can be infinitely many tangents to a circle. Question 2. Fill in the blanks: (i) A tangent to a circle intersects it in ………… point(s). (ii) A line intersecting a circle in two points is called a ………… . (iii) A circle […]
Chapter 9 Some Applications of Trigonometry Ex 9.1
Chapter 9 Some Applications of Trigonometry Ex 9.1 Question 1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° […]
Chapter 8 Introduction to Trigonometry Ex 8.4
Chapter 8 Introduction to Trigonometry Ex 8.4 Question 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. Solution: From trigonometric identity, cosec² A – cot² A = 1, we get Question 2. Write all the other trigonometric ratios of ∠A in terms of sec A. Solution: Since […]
Chapter 8 Introduction to Trigonometry Ex 8.3
Chapter 8 Introduction to Trigonometry Ex 8.3 Question 1. Solution: Question 2. Show that: (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° – sin 38° sin 52° = 0 Solution: (i) LHS = tan 48° tan 23° tan 42° tan 67° = tan 48° tan 23° tan […]