Sujeet Kumar

Question 1.Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.Solution:Let the two circles having centres P and Q touch each other internally at point R.Here, QR = 3.5 cm, PR = 4.8 cmThe two circles touch each other internally.∴ By theorem of touching circles,P – … Read more

Question 1.In the adjoining figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.i. What is the measure of ∠CAB? Why?ii. What is the distance of point C from line AB? Why?iii. d(A, B) = 6 cm, find d(B, C).iv. What is … Read more

Question 1.Some questions and their alternative answers are given. Select the correct alternative. [1 Mark each] i. Out of the following which is the Pythagorean triplet?(A) (1,5,10)(B) (3,4,5)(C) (2,2,2)(D) (5,5,2)Answer: (B)Hint: Refer Practice set 2.1 Q.1 (i) ii. In a right angled triangle, if sum of the squares of the sides making right angle is 169, … Read more

Question 1.In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.Solution:In ∆PQR, point S is the midpoint of side QR. [Given]∴ seg PS is the median.∴ PQ2 + PR2 = 2 PS2 + 2 SR2 [Apollonius theorem]∴ 112 + 172 = 2 (13)2 + 2 SR2∴ 121 + 289 = … Read more

Question 1.Identify, with reason, which of the following are Pythagorean triplets.i. (3,5,4)ii. (4,9,12)iii. (5,12,13)iv. (24,70,74)v. (10,24,27)vi. (11,60,61)Solution:i. Here, 52 = 2532 + 42 = 9 + 16 = 25∴ 52 = 32 + 42The square of the largest number is equal to the sum of the squares of the other two numbers.∴ (3,5,4) is a Pythagorean triplet. ii. Here, 122 = … Read more

Question 1.Select the appropriate alternative.(A) ∆PQR – ∆ABC(B) ∆PQR – ∆CAB(C) ∆CBA – ∆PQR(D) ∆BCA – ∆PQRAnswer:(B) ii. If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E, then which of the following statements is false? iii. In ∆ABC and ∆DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE, then which … Read more

Question 1.The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.Solution:Let the corresponding sides of similar triangles be S1 and S2.Let A1 and A2 be their corresponding areas.∴ Ratio of areas of similar triangles = 9 : 25 Question 2.If ∆ABC ~ ∆PQR and AB : PQ = 2:3, … Read more

Question 1.In the adjoining figure, ∠ABC = 75°, ∠EDC = 75°. State which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.Solution:In ∆ABC and ∆EDC,∠ABC ≅ ∠EDC [Each angle is of measure 75°]∠ACB ≅ ∠ECD [Common angle]∴ ∆ABC ~ ∆EDC [AA … Read more

Question 1.Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of ∠QPR.Solution: Question 2.In ∆PQR PM = 15, PQ = 25, PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason. Solution:PN + NR = PR [P – … Read more

Question 1.Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.Solution:Let the base, height and area of the first triangle be b1, h1, and A1 respectively.Let the base, height and area of the second triangle be b2, h2 and … Read more