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. A regular polygon with (2m + 1) sides has each interior angle equal to 144°. The value of m is58109/22. Which of the following statements is false?If two triangles are similar, then they are also congruentAn equiangular triangle is also equilateralAn equilateral triangle is also equiangularIf two triangles are congruent, then they are also similar3. In the figure given below, ABCD is a rectangle. The area of the isosceles right triangle ABE = 7cm^{2}; EC = 3(BE). The area of ABCD (in cm^{2}) is 28 cm²56 cm²42 cm²21 cm²4. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD=∠BAC∠BCD=∠BAC What is the ratio of the perimeter of ΔADCΔADC to that of the ΔBDCΔBDC? 7/96/98/95/95. Find the total surface area of a closed conical container with radius 5 cm and a height of 15 cm.420 sq. cm327 sq. cm124 sq. cm209 sq. cm6. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?13575901507. Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is25556201410248. A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30π30π km/hr on the OR road, 20π20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. The ratio of the sum of the lengths of all chord roads to the length of the outer ring road is √5:25: π√5:2π√5:π9. A cube has a total surface area of the six faces equal to 150 square feet. What is the volume of the cube?356712532110. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?102114511. Find the size of angle x in the figure below84°24°36°56°12. The vertices of the inscribed (inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square.1:42:31:32:113. In the adjoining figure I and II, are circles with P and Q respectively, The two circles touch each other and have common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm. What is the ratio of the length of PQ to that of QO?1:31:43:83:414. The parallelogram shown in the figure below has a perimeter of 44 cm and an area of 64 cm^{2}. Find angle T in degrees.64°55.2°12.3°34.8°15. 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 inches45 inches√119 inches√59 inches16. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠∠ CBE = 65^{0}, then what is the value of ∠∠DEC? 35°25°55°45°17. What is the number of distinct triangles with integral valued sides and perimeter 14?543618. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq. cm.) of the intersecting region?π/3 - √3/4π/3 - 2/34π/3 - √3/42π/3 - √3/219. 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 x3h²=2b²2h²=b²3b²=2h²2b²=h²20. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is 100°150°80°2°21. A point X is equidistant from two fixed points P and Q. The locus of X is theperpendicular to the line PQperpendicular bisector of line PQparallel line to line PQparallel lines to PQ on either side of line PQ22. Find the volume of a closed conical container with radius 5 cm and a height of 15 cm.39348312425423. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is2/33/41/21/424. 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 is10 cm12 cm20 cm8 cm25. In the adjoining figure I and II, are circles with P and Q respectively, The two circles touch each other and have common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm. The length of SO is10√3 cm12√3 cm14√3 cm8√3 cm26 out of 25Time is Up!