If the non parallel sides of a trapezium are equal,prove that it is cyclic.

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- Q) prove that angles in the same segment of a circle are equal
- Q) if two non parallel sides of a trapezium are equal prove that it is cyclic
- Q) question 1: ( 1.0 marks) what is the value ofkfor which (27, −7) is a solution of the equation 3x+ky= 25? a. 8 b. 7 c. 6 d. 5 question 2: ( 1.0 marks) what is the distance between the linesx− 10 = 0 andx+ 2 = 0? a. 2 units b. 8 units c. 10 units d. 12 units question 3: ( 1.0 marks) in a cyclic quadrilateral abcd, ∠cdb measures 25° and ∠dac measures 70°. what is the measure of ∠bcd? a. 75° b. 85° c. 95° d. 105° question 4: ( 1.0 marks) a cylinder and a cone have the same radius and the height of the cone is thrice the height of the cylinder. what is the ratio of the volume of the cylinder to that of cone? a. 1: 1 b. 1: 2 c. 2: 3 d. 3: 2 question 5: ( 1.0 marks) use the following information to answer the next question. what is the measure of ∠acb? a. 15° b. 20° c. 30° d. 35° question 6: ( 1.0 marks) p, q, r and s are the respective mid-points of the sides ab, bc, cd and ad of quadrilateral abcd. if ac = 10 cm and bd = 8 cm, then what is the perimeter of quadrilateral pqrs? a. 16 cm b. 18 cm c. 24 cm d. 36 cm question 7: ( 1.0 marks) use the following information to answer the next question. . if the area of parallelogram abcd is 184 cm2, then what is the area of the shaded region? a. 92 cm2 b. 98 cm2 c. 124 cm2 d. 138 cm2 question 8: ( 1.0 marks) if the mean of the data 6, 8, 5, 5, 0,x+ 6,x,x+ 6, 0, 8 is 2x+ 1, then what is the value ofx? a. 2 b. 1 c. −1 d. −2 question 9: ( 2.0 marks) use the following information to answer the next question. in the given figure, ad is the diameter of the circle with centre o. what is the measure of ∠cpd in the given figure? a. 30° b. 40° c. 50° d. 60° question 10: ( 2.0 marks) use the following information to answer the next question. sixty students were chosen at random from a particular village to know the distance of their school from their respective homes. the information gathered is given in the form of frequency distribution table as: distance (in km) number of students 0 − 5 30 5 − 10 11 10 − 15 10 15 or more 9 if a student is chosen at random from the village, then what is the probability that his/her school is 5 km or more farther from his/her house? a. b. c. d. question 11: ( 2.0 marks) if the diameter of a hemispherical bowl is equal to the edge of a cubical vessel, then what is the ratio of the capacities of the hemispherical bowl and the cubical vessel? a. 11:42 b. 3:8 c. 13:9 d. 14:11 question 12: ( 2.0 marks) use the following information to answer the next question. in the given figure, abce is a trapezium and aedc is a rectangle. if the area of triangle bec is 72 cm 2 , then what is the area of quadrilateral bcde? a. 92 cm 2 b. 144 cm 2 c. 122 cm 2 d. 130 cm 2 question 13: ( 2.0 marks) three times the number of chocolates with anil is 8 more than five times the number of chocolates that aarti has. if the number of chocolates that anil and aarti have arexandyrespectively, then find an equation satisfying the given information. question 14: ( 2.0 marks) the mean of the given data is3.48.find the value ofm? x i f i 1 18 2 17 3 m 4 6 5 16 6 21 question 15: ( 2.0 marks) use the following information to answer the next question. the given table shows the number of t-shirts sold out from a shop for each size of a particular brand during an ongoing festive season. size of t-shirt 36 38 40 42 44 number of t-shirts sold 54 57 80 39 30 what is the probability that the t-shirt which will be sold next is of size 42? question 16: ( 2.0 marks) use the following information to answer the next question. a survey is conducted across 1000 families to find out the number of boy child in a family. the given data shows the findings of the survey: number of boys in the family 0 1 2 3 number of families 205 310 435 50 what is the probability that a family chosen at random has at most 2 boys? question 17: ( 2.0 marks) a conical tent is made up of 251.2 square feet of canvas. if the diameter of the tent is 16 m, then find the height of the tent. [use π = 3.14] question 18: ( 2.0 marks) the given figure represents a rectangle abcd such that ab = 6 cm and bc = 8 cm. p and q are the mid-points of the sides ab and bc respectively. find the length of br. question 19: ( 2.0 marks) use the following information to answer the next question. in the given figure, abcd and abef are parallelograms. prove that (i)area (abcd) = area (abef) (ii) question 20: ( 3.0 marks) use the following information to answer the next question. in the given figure, δabc is equilateral and bc||eg||ad. e is the mid-point of bd. if ad = 5 cm, bd = 12 cm, then find the ratio ad: eg: bc. question 21: ( 3.0 marks) in the given figure, abcd is a rectangle of dimension 20 cm and 26 cm and acef is a parallelogram. find the area of the parallelogram acef. question 22: ( 3.0 marks) the given figure shows a circle with centre o. a, b, c, and d are points on the circle such that ab = 16 cm. if cd = 30 cm, then find the distance of the chord cd from the centre. question 23: ( 3.0 marks) the floor of a rectangular room has dimensions 5 m × 4 m. the height of the room is 3.5 m. the room has one rectangular door and two rectangular windows. the door has dimensions 200 cm × 80 cm and each window has dimensions 120 cm × 150 cm. find the cost of painting the inner walls of the room at the rate of rs 12.50 per m 2 . question 24: ( 3.0 marks) the lateral surface area and the area of the base of a cone are in the ratio 5:4. if the volume of the cone is 1024 π m 3 , then find the height of the cone. question 25: ( 3.0 marks) the given figure represents a trapezium abcd in which ad || bc. p and q are the mid-points of diagonals bd and ac respectively. find the perimeter of trapezium abcd. question 26: ( 3.0 marks) the given figure represents a trapezium pqrs in which ps||qr. a and b are the mid-points of ps and sr respectively. pbxr is a parallelogram. if area (δapq) = 24 cm 2 , then find the area of parallelogram pbxr. question 27: ( 3.0 marks) if the point (−1, 3) is the point of intersection of the lines, 2x+ 3y−k= 0 and kx+py+ 1 = 0, then find the value ofp. question 28: ( 3.0 marks) check whether the line passes through the point of intersection of the lines,and. question 29: ( 3.0 marks) 114 electrical components were selected at random from a factory as sample. the given frequency table lists the observed lifetimes of the selected electrical components. lifetime (in hours) number of electrical components 0 − 15 16 15 − 30 10 30 − 45 24 45 − 60 31 60 − 75 11 75 − 90 12 90 − above 10 what is the probability of anelectrical componentchosen at random having lifetime more than or equal to 45 hours? question 30: ( 4.0 marks) a cylindrical container can hold a maximum of 3 l 80 ml milk. a new container is made by decreasing the base diameter of the original container by 20% and increasing its height by 25%. find the maximum amount of milk that the new container can hold. question 31: ( 4.0 marks) if 3 is added to the numerator and denominator of a rational number, then the number becomes. determine the denominator graphically if the numerator is 3. question 32: ( 4.0 marks) the given table shows the salary of 60 workers at a small factory. draw the frequency polygon of this data. salary number of workers 3000 − 4000 4000 − 5000 5000 − 6000 6000 − 7000 15 25 9 11 question 33: ( 4.0 marks) a, b, c, and d are the respective mid-points of the sides pq, qr, rs, and sp of a rhombus pqrs where the vertices are taken in order. if the area of quadrilateral abcd formed is 60 cm 2 , then find the area of rhombus pqrs. question 34: ( 4.0 marks) construct a δabc in which bc = 7 cm, ∠b = 60°, and ab + ac = 12 cm. we strongly recommend you to finish the test before viewing the solution , in order to get the maximum benifit. view solutions later proceed to solutions « prev next » finish » question 1: ( 1.0 marks) what is the value ofkfor which (27, −7) is a solution of the equation 3x+ky= 25? a. 8 b. 7 c. 6 d. 5 question 2: ( 1.0 marks) what is the distance between the linesx− 10 = 0 andx+ 2 = 0? a. 2 units b. 8 units c. 10 units d. 12 units question 3: ( 1.0 marks) in a cyclic quadrilateral abcd, ∠cdb measures 25° and ∠dac measures 70°. what is the measure of ∠bcd? a. 75° b. 85° c. 95° d. 105° question 4: ( 1.0 marks) a cylinder and a cone have the same radius and the height of the cone is thrice the height of the cylinder. what is the ratio of the volume of the cylinder to that of cone? a. 1: 1 b. 1: 2 c. 2: 3 d. 3: 2 question 5: ( 1.0 marks) use the following information to answer the next question. what is the measure of ∠acb? a. 15° b. 20° c. 30° d. 35° question 6: ( 1.0 marks) p, q, r and s are the respective mid-points of the sides ab, bc, cd and ad of quadrilateral abcd. if ac = 10 cm and bd = 8 cm, then what is the perimeter of quadrilateral pqrs? a. 16 cm b. 18 cm c. 24 cm d. 36 cm question 7: ( 1.0 marks) use the following information to answer the next question. . if the area of parallelogram abcd is 184 cm2, then what is the area of the shaded region? a. 92 cm2 b. 98 cm2 c. 124 cm2 d. 138 cm2 question 8: ( 1.0 marks) if the mean of the data 6, 8, 5, 5, 0,x+ 6,x,x+ 6, 0, 8 is 2x+ 1, then what is the value ofx? a. 2 b. 1 c. −1 d. −2 question 9: ( 2.0 marks) use the following information to answer the next question. in the given figure, ad is the diameter of the circle with centre o. what is the measure of ∠cpd in the given figure? a. 30° b. 40° c. 50° d. 60° question 10: ( 2.0 marks) use the following information to answer the next question. sixty students were chosen at random from a particular village to know the distance of their school from their respective homes. the information gathered is given in the form of frequency distribution table as: distance (in km) number of students 0 − 5 30 5 − 10 11 10 − 15 10 15 or more 9 if a student is chosen at random from the village, then what is the probability that his/her school is 5 km or more farther from his/her house? a. b. c. d. question 11: ( 2.0 marks) if the diameter of a hemispherical bowl is equal to the edge of a cubical vessel, then what is the ratio of the capacities of the hemispherical bowl and the cubical vessel? a. 11:42 b. 3:8 c. 13:9 d. 14:11 question 12: ( 2.0 marks) use the following information to answer the next question. in the given figure, abce is a trapezium and aedc is a rectangle. if the area of triangle bec is 72 cm 2 , then what is the area of quadrilateral bcde? a. 92 cm 2 b. 144 cm 2 c. 122 cm 2 d. 130 cm 2 question 13: ( 2.0 marks) three times the number of chocolates with anil is 8 more than five times the number of chocolates that aarti has. if the number of chocolates that anil and aarti have arexandyrespectively, then find an equation satisfying the given information. question 14: ( 2.0 marks) the mean of the given data is3.48.find the value ofm? x i f i 1 18 2 17 3 m 4 6 5 16 6 21 question 15: ( 2.0 marks) use the following information to answer the next question. the given table shows the number of t-shirts sold out from a shop for each size of a particular brand during an ongoing festive season. size of t-shirt 36 38 40 42 44 number of t-shirts sold 54 57 80 39 30 what is the probability that the t-shirt which will be sold next is of size 42? question 16: ( 2.0 marks) use the following information to answer the next question. a survey is conducted across 1000 families to find out the number of boy child in a family. the given data shows the findings of the survey: number of boys in the family 0 1 2 3 number of families 205 310 435 50 what is the probability that a family chosen at random has at most 2 boys? question 17: ( 2.0 marks) a conical tent is made up of 251.2 square feet of canvas. if the diameter of the tent is 16 m, then find the height of the tent. [use π = 3.14] question 18: ( 2.0 marks) the given figure represents a rectangle abcd such that ab = 6 cm and bc = 8 cm. p and q are the mid-points of the sides ab and bc respectively. find the length of br. question 19: ( 2.0 marks) use the following information to answer the next question. in the given figure, abcd and abef are parallelograms. prove that (i)area (abcd) = area (abef) (ii) question 20: ( 3.0 marks) use the following information to answer the next question. in the given figure, δabc is equilateral and bc||eg||ad. e is the mid-point of bd. if ad = 5 cm, bd = 12 cm, then find the ratio ad: eg: bc. question 21: ( 3.0 marks) in the given figure, abcd is a rectangle of dimension 20 cm and 26 cm and acef is a parallelogram. find the area of the parallelogram acef. question 22: ( 3.0 marks) the given figure shows a circle with centre o. a, b, c, and d are points on the circle such that ab = 16 cm. if cd = 30 cm, then find the distance of the chord cd from the centre. question 23: ( 3.0 marks) the floor of a rectangular room has dimensions 5 m × 4 m. the height of the room is 3.5 m. the room has one rectangular door and two rectangular windows. the door has dimensions 200 cm × 80 cm and each window has dimensions 120 cm × 150 cm. find the cost of painting the inner walls of the room at the rate of rs 12.50 per m 2 . question 24: ( 3.0 marks) the lateral surface area and the area of the base of a cone are in the ratio 5:4. if the volume of the cone is 1024 π m 3 , then find the height of the cone. question 25: ( 3.0 marks) the given figure represents a trapezium abcd in which ad || bc. p and q are the mid-points of diagonals bd and ac respectively. find the perimeter of trapezium abcd. question 26: ( 3.0 marks) the given figure represents a trapezium pqrs in which ps||qr. a and b are the mid-points of ps and sr respectively. pbxr is a parallelogram. if area (δapq) = 24 cm 2 , then find the area of parallelogram pbxr. question 27: ( 3.0 marks) if the point (−1, 3) is the point of intersection of the lines, 2x+ 3y−k= 0 and kx+py+ 1 = 0, then find the value ofp. question 28: ( 3.0 marks) check whether the line passes through the point of intersection of the lines,and. question 29: ( 3.0 marks) 114 electrical components were selected at random from a factory as sample. the given frequency table lists the observed lifetimes of the selected electrical components. lifetime (in hours) number of electrical components 0 − 15 16 15 − 30 10 30 − 45 24 45 − 60 31 60 − 75 11 75 − 90 12 90 − above 10 what is the probability of anelectrical componentchosen at random having lifetime more than or equal to 45 hours? question 30: ( 4.0 marks) a cylindrical container can hold a maximum of 3 l 80 ml milk. a new container is made by decreasing the base diameter of the original container by 20% and increasing its height by 25%. find the maximum amount of milk that the new container can hold. question 31: ( 4.0 marks) if 3 is added to the numerator and denominator of a rational number, then the number becomes. determine the denominator graphically if the numerator is 3. question 32: ( 4.0 marks) the given table shows the salary of 60 workers at a small factory. draw the frequency polygon of this data. salary number of workers 3000 − 4000 4000 − 5000 5000 − 6000 6000 − 7000 15 25 9 11 question 33: ( 4.0 marks) a, b, c, and d are the respective mid-points of the sides pq, qr, rs, and sp of a rhombus pqrs where the vertices are taken in order. if the area of quadrilateral abcd formed is 60 cm 2 , then find the area of rhombus pqrs. question 34: ( 4.0 marks) construct a δabc in which bc = 7 cm, ∠b = 60°, and ab + ac = 12 cm. we strongly recommend you to finish the test before viewing the solution , in order to get the maximum benifit. view solutions later proceed to solutions « prev next »
- Q) prove that the sum of either pair of opposite angles of a cyclicquadrilateral is 180º.
- Q) prove that the quadrilateral formed by internal angle bisectors of a cyclic quadrilateral is also cyclic.