Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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 radius of the circle II? 3 cm 4 cm 5 cm 2 cm 2. Which of the following statements is false? If two triangles are similar, then they are also congruent An equiangular triangle is also equilateral If two triangles are congruent, then they are also similar An equilateral triangle is also equiangular 3. If a, b and c are the sides of a triangle, and a2+ b2+ c2= bc + ca + ab, then the triangle is Equilateral Isosceles obtuse-angled right-angled 4. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.What is the area, in square inches, of the base of the pyramid? 220 sq. inches 120 sq. inches 200 sq. inches 100 sq. inches 5. 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 <span id="MathJax-Element-47-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="30π">30π30π km/hr on the OR road, <span id="MathJax-Element-48-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="20π">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:π √5:2π 5: π √5:2 6. Which two angles are not supplementary? 5 degrees and 175 degrees 23 degrees and 177 degrees 30 degrees and 150 degrees 89 degrees and 91 degrees 7. The parallelogram shown in the figure below has a perimeter of 44 cm and an area of 64 cm2. Find angle T in degrees. 55.2° 64° 12.3° 34.8° 8. The sides /AB/ and /AC/ of a triangle ABC are produced to D and E respectively such that <DBC = 125° and <BCE = 95°. Find the value of <BAC 40 degrees 90 degrees 85 degrees 55 degrees 9. 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. 17 cm 19 cm 21 cm 12 cm 10. Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. 768 m² 696.5 m² 684 m² 534 m² 11. Consider three circular parks of equal size with centers at A1, A2, and A3 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 A1A2A3, B1B2B3, and C1C2C3, , as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1respectively. 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 = c+a/2 = 2(1+√3)r b-a = c-b = √3r b-a = c-b = 3√3r c = 2b-a = (2+√3)r 12. 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° 2° 150° 80° 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 3 1 0 2 14. The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is 24 cm 20 cm 25 cm 15 cm 15. Four of five interior angles of a pentagon are equal. If the size of the fifth angle is 80°, then the size of each of the four equal angles is 100 degrees 120 degrees 136 degrees 115 degrees 16. Two chords AC and BD of a circle intersect inside the circle at E. If <BAC = 35°, <CAD = 42° and <ABD = 70°, find <ACB. 70 degrees 77 degrees 33 degrees 42 degrees 17. Based on the figure below, what is the value of x, if y = 10? 13 12 10 11 18. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees? 150 90 75 135 19. 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)/ 4 (6-π)/ 8 (x+2)/ 8 (4-π)/ 4 20. 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 30π km/hr on the OR road, 20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to reach E2 from N1 using first the chord N1 – W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question? 45 60 105 90 21. 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 one of the statements alone but not by the other. The question cannot be answered even by using both the statements together. The question can be answered by using both the statements together, but cannot be answered by using either statement alone. The question can be answered by using either statement alone. 22. 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 is 1024 255 56 2014 23. 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 be 32π 40.5π 81π 50π 24. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.Using the height as √119 inches , what is the volume, in cubic inches, of the pyramid? 135 238 432 363.6 25. In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If ∠D=400, then ∠ACB = 70 20 100 140 1 out of 25 Time is Up! Time's up