Sujeet Kumar

Question 1. Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines.i. 45°ii. 60°iii. 90°Solution:i. Angle made with the positive direction ofX-axis (θ) = 45°Slope of the line (m) = tan θ∴ m = tan 45° = 1∴ The slope of the line is 1. ii. … Read more

Question 1.Find the co-ordinates of point P if P divides the line segment joining the points A (-1, 7) and B (4, -3) in the ratio 2:3.Solution:Let the co-ordinates of point P be (x, y) and A (x1, y1) B (x2, y2) be the given points.Here, x1 = -1, y1 = 7, x2 = 4, y2 = -3, m … Read more

Question 1. Find the distance between each of the following pairs of points.i. A (2, 3), B (4,1)ii. P (-5, 7), Q (-1, 3)iii. R (0, -3), S (0,52)iv. L (5, -8), M (-7, -3)v. T (-3, 6), R (9, -10)Solution:i. Let A (x1, y1) and B (x2, y2) be the given points.∴ x1 = 2, … Read more

Question 1.Select the correct alternative for each of the following questions. i. The number of tangents that can be drawn to a circle at a point on the circle is ______(A) 3(B) 2(C) 1(D) 0Answer:(C) ii. The maximum number of tangents that can be drawn to a circle from a point outside it is ______(A) … Read more

Question 1.Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.Solution:Analysis:seg PM ⊥ line l ….[Tangent is perpendicular to radius]The perpendicular to seg PM at point M will give the required tangent at M. Question 2.Draw a circle of radius 2.7 cm. Draw a tangent to … Read more

Question 1.Solution:Analysis: Question 2. Solution:Analysis:As shown in the figure, Let R – P – L and R – Q – T.∆PQR ~ ∆LTR … [Given]∴ ∠PRQ ≅ ∠LRT … [Corresponding angles of similar triangles]∴ sides of LTR are longer than corresponding sides of ∆PQR.If seg QR is divided into 3 equal parts, then seg TR … Read more

Question 1.Four alternative answers for each of the following questions are given. Choose the correct alternative. i. Two circles of radii 5.5 cm and 3.3 cm respectively touch each other. What is the distance between their centres?(A) 4.4 cm(B) 8.8 cm(C) 2.2 cm(D) 8.8 or 2.2 cmAnswer: (D)Two circles can touch each other internally or externally.∴ … Read more

Question 1.In the adjoining figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.Solution:i. Ray PQ is a tangent to the circle at point Q and seg PS is the secant. [Given]∴ PR × PS = PQ2 [Tangent secant segments theorem]∴ 8 × PS = 122∴ 8 … Read more

Question 1.In the adjoining figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.i. ∠AOBii. ∠ACBiii. arc ABiv. arc ACB.Solution:i. seg OA = seg OB = radius…… (i) [Radii of the same circle]seg AB = radius…… (ii) [Given]∴ seg … Read more

Question 1.In the adjoining figure, points G, D, E, F are concyclic points of a circle with centre C.∠ECF = 70°, m(arc DGF) = 200°. Find m(arc DE) and m(arc DEF).Solution:m(arc EF) = m∠ECF [Definition of measure of minor arc]∴ m(arc EF) = 70°i. m(arc DE) + m(arc DGF)+ m(arc EF) = 360° [Measure of … Read more