Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point between A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divide the parallelogram in two regions with equal areas.12 cm21 cm17 cm19 cm2. AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle? A. AB is not a diameter of the circle. B. The distance between AB and the tangent at E is 5 cm.The question can be answered by using either statement alone.The question can be answered by using both the statements together, but cannot be answered by using either statement alone.The question cannot be answered even by using both the statements together.The question can be answered by one of the statements alone but not by the other.3. If a, b and c are the sides of a triangle, and a^{2}+ b^{2}+ c^{2}= bc + ca + ab, then the triangle isobtuse-angledright-angledIsoscelesEquilateral4. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?10215145. Find the area of the given shape.270 sq. cm298 sq. cm183 sq. cm309 sq. cm6. When two straight lines intersectÂ I. adjacent angles are equalÂ II. adjacent angles are supplementaryÂ III. vertically opposite angles are equalIV. vertically opposite angles are supplementaryÂ Which of the above statements are true?I and IV onlyII and IV onlyII and III onlyI and III only7. Consider a circle with unit radius. There are seven adjacent sectors, S_{1}, S_{2}, S_{3}, ..., S_{7}, in the circle such that their total area isÂ 1818of the area of the circle. Further, the area of the j^{th}Â sector is twice that of the (j â€“ 1)^{th}Â sector, for j = 2, ..., 7. What is the angle, in radians, subtended by the arc of S_{1} at the centre of the circle?Ï€/2040Ï€/1524Ï€/508Ï€/10168. 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?25458559. 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 30Ï€ km/hr on the OR road, 20Ï€ km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 â€“ E1 on OR, and then on the chord road E1 â€“ N2. What is the radius of the outer ring road in kms?2040603010. Which two angles areÂ not supplementary?5 degrees and 175 degreesÂ 30 degrees and 150 degreesÂ 89 degrees and 91 degreesÂ 23 degrees and 177 degrees11. ABC is a right triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB.35Â°148Â°135Â°94Â°12. The interior angles of a polygon add up tp 1980Â°. How many sides has the polygon?1012151313. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?Between 0 and 60Between 0 and 90Between 0 and 30Between 0 and 7514. Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90Â° or concave if the internal angle is 270Â°. If the number of convex corners in such a polygon is 25, the number of concave corners must be220212015. The sides /AB/ and /AC/ of a triangle ABC are produced to D and E respectively such thatÂ <DBC = 125Â° and <BCE = 95Â°. Find the value of <BAC40 degrees55 degrees90 degrees85 degrees16. In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to1:14:13:83:217. In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. InÂ Î”ARCÎ”ARC, âˆ ARC =90^{0}Â and inÂ Î”PQSÎ”PQS, âˆ PSQ =90^{0}The length of QS is 6 cm. What is the ratio of AP : PD? 10:38:32:37:318. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?3 or 212 or 144 or 281 or 719. In the figure (not drawn to scale) given below, if AD = CD = BC and âˆ BCE =96^{0}Â , how much is the value of âˆ DBC? 64Â°32Â°28Â°84Â°20. In the figure below triangle OAB has an area of 72 and triangle ODC has an area of 288. Find x and y, respectively.9, 4312, 3420, 1423, 4321. 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.55.2Â°64Â°34.8Â°12.3Â°22. A cube has a total surface area of the six faces equal to 150 square feet. What is the volume of the cube?321671253523. A regular polygon with (2m + 1) sides has each interior angle equal to 144Â°. The value of m is85109/224. In the above diagram,Â âˆ ABC=90âˆ˜=âˆ DCH=âˆ DOE=âˆ EHK=âˆ FKL=âˆ GLM=âˆ LMNâˆ ABC=90âˆ˜=âˆ DCH=âˆ DOE=âˆ EHK=âˆ FKL=âˆ GLM=âˆ LMN AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN The magnitude of âˆ FGO =30Â°60Â°45Â°none of the above25. Which of the following is not an exterior angle of a regular polygon?18 degrees15 degrees24 degrees21 degrees26 out of 25Time is Up!