26/03/2020 Geometry(Study by Topics Senior Class) 0Comments by Gate Academy Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?52585452. In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90° . If AB:CD = 3:1, the ratio of CD: PQ is 1 :0.751:0.691: 0.720.5 : 13. In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ∠ACD = y degrees and ∠AOD = x degrees such that x = ky, then the value of k is 03124. Each interior angle of an eight sided polygon is equal to135 degrees140 degrees130 degrees120 degrees5. A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city12 km4 km6km9 km6. In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm? 40 cm10 cm20 cm50 cm7. Find the measure of angle A in the figure below.103°51°98°87°8. All the vertices of an isosceles triangle lie on a circle and each of the base angles of the triangle is 65°. The angle subtended at the centre of the circle by the base of the triangle is65 degrees100 degrees130 degrees115 degrees9. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?521101410. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?150135759011. ABC is a right triangle. AM is perpendicular to BC. The size of angle ABC is equal to 55 degrees. Find the size of angle MAC.106°65°75°55°12. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.What is h, the height, in inches, of the pyramid?√35 inches√119 inches45 inches√59 inches13. A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal ofthe square. The proportion of the sheet area that remains after punching is:(x+2)/ 8(4-π)/ 4(6-π)/ 8(x-2)/ 414. A point P moves such that it is always equidistant from two fixed points X and Y. When /XY/ is 12 cm and P is 8 cm from /XY/, the distance of P from Y is8 cm12 cm20 cm10 cm15. Consider three circular parks of equal size with centers at A^{1}, A^{2}, and A^{3} respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A^{1}A^{2}A^{3}, B^{1}B^{2}B^{3}, and C^{1}C^{2}C^{3}, , as shown. Three sprinters A, B, and C begin running from points A^{1}, B^{1} and C^{1}respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point. Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a, b and c respectively. Which of the following is true?b-a = c-b = √3rb = c+a/2 = 2(1+√3)rb-a = c-b = 3√3rc = 2b-a = (2+√3)r16. A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm) will be32π40.5π50π81π17. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC? 64°32°84°28°18. A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose ∠APB = 60° then the relationship between h and b can be expressed as x2h²=b²2b²=h²3b²=2h²3h²=2b²19. The interior angles of a polygon add up tp 1980°. How many sides has the polygon?1213101520. Find the size of angle x in the figure below36°24°56°84°21. A point X is equidistant from two fixed points P and Q. The locus of X is theperpendicular bisector of line PQparallel lines to PQ on either side of line PQparallel line to line PQperpendicular to the line PQ22. Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from square cloth piece of side a in the following steps: the original square of side a is divided into nsmaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is1:1√2:14n-π/ (4-π)n(4-π)/ 4n-π23. Which of the following specified sets of data is not necessarily sufficient for the construction of a triangle?Two sides and an included angleThree sidesTwo sides and a right angleThree angle24. Which two angles are complementary?58 degrees and 22 degrees 67 degrees and 23 degrees21 degrees and 78 degrees140 degrees and 40 degrees25. Find the area of the given shape.270 sq. cm183 sq. cm309 sq. cm298 sq. cm26 out of 25Time is Up! Time's up