This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Q1 A. Choose the correct alternative for the following questions: i) The circle which passes through all the vertices of a triangle is called A circle that passes through all the vertices of a triangle is called a circumcircle. The correct option is (A) circumcircle. ii) Any point on the line y=x is of the form For any point on the line y=x, its x-coordinate and y-coordinate are equal. Therefore, a point on this line is of the form (a, a). The correct option is (A) (a,a). iii) Which of the following is the value of 90^? The value of 90^ is 1. The correct option is (D) 1. iv) 2 45^ + 45^ - 45^ Step 1: Recall the values of the trigonometric functions. 45^ = 1 45^ = (1)/(sqrt(2)) 45^ = (1)/(sqrt(2)) Step 2: Substitute the values into the expression. 2 45^ + 45^ - 45^ = 2(1) + (1)/(sqrt(2)) - (1)/(sqrt(2)) Step 3: Simplify the expression. 2(1) + (1)/(sqrt(2)) - (1)/(sqrt(2)) = 2 + 0 = 2 The correct option is (C) 2. Q1 B. Solve the following. i) If the radius of a circle is 4cm, then find the diameter? Step 1: The relationship between radius (r) and diameter (d) is d = 2r. Step 2: Substitute the given radius r = 4 cm. d = 2 × 4 cm d = 8 cm The diameter is 8 cm. ii) What is the equation of Y-axis? The Y-axis is the vertical line where the x-coordinate of every point is 0. The equation of the Y-axis is x=0. iii) Find the value of 45^? The value of 45^ is 1. The value is 1. iv) Find the volume of a cube if length = 1cm? Step 1: The formula for the volume (V) of a cube with side length (s) is V = s^3. Step 2: Substitute the given length s = 1 cm. V = (1 cm)^3 V = 1 cm^3 The volume of the cube is 1 cm^3. Q.2(A) Complete 2 activities out of 3. (4marks) i) Radius of a circle is 20cm. Distance of a chord from the centre of a circle is 12cm. Find the length of the chord. Solution: Let the centre of the circle be O. Radius = OD = 20 cm. Distance of the chord CD from O is 12 cm. seg OP seg CD. OP = 12 cm Now CP = 16 cm (perpendicular drawn from the centre bisects the chord). In the right angled OPD, using Pythagoras' theorem OP^2 + PD^2 = OD^2. Step 1: Substitute the known values into the Pythagorean theorem. 12^2 + PD^2 = 20^2 Step 2: Calculate the squares. 144 + PD^2 = 400 Step 3: Solve for PD^2. PD^2 = 400 - 144 PD^2 = 256 Step 4: Find PD by taking the square root. PD = sqrt(256) PD = 16 cm Step 5: Since the perpendicular from the center bisects the chord, CD = 2 × PD. CD = 2 × 16 cm CD = 32 cm The length of the chord is 32 cm.