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. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?13575901502. 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 90Between 0 and 30Between 0 and 60Between 0 and 753. 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 is12√3 cm8√3 cm14√3 cm10√3 cm4. Which of the following is not an exterior angle of a regular polygon?24 degrees18 degrees15 degrees21 degrees5. Two identical circles intersect so that their centers, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles isππ/5π/4 -1π/46. 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?45852557. 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?1:43:41:33:88. A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?15 m10 m20 m17 m9. 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.696.5 m²534 m²768 m²684 m²10. On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC? 75715511. In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the ΔACDΔACD and ΔBCDΔBCD. P and Q are the centres of the circles. The distance PQ is 875√5012. 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?45609010513. 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 √5:2π√5:25: π√5:π14. 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 = 3√3rb = c+a/2 = 2(1+√3)rc = 2b-a = (2+√3)rb-a = c-b = √3r15. In ΔABCΔABC, the internal bisector of ∠A∠A meets BCBC at DD. If AB=4,AC=3 and ∠A=60° AB=4,AC=3 and∠A=60∘, then the length of ADAD is15√3/ 812√3/ 72√36√3/ 716. In a regular pentagon ABCDE, /AC/ intersects /BD/ at F. Calculate <CBD.108 degrees72 degrees36 degrees60 degrees17. 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?135432238363.618. Two chords AC and BD of a circle intersect inside the circle at E. If <BAC = 35°, <CAD = 42° and <ABD = 70°, find <ACB.77 degrees33 degrees70 degrees42 degrees19. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10.Its area is 80. What is the exact length of its third side√250√290√270√26020. 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 is1/43/41/22/321. 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=2b²2b²=h²2h²=b²3b²=2h²22. What is the number of distinct triangles with integral valued sides and perimeter 14?635423. Find the size of angle MBD in the figure below55°72°79°23°24. 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 - 2/32π/3 - √3/2π/3 - √3/44π/3 - √3/425. 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. In ΔARCΔARC, ∠ARC =90^{0} and in ΔPQSΔPQS, ∠PSQ =90^{0}The length of QS is 6 cm. What is the ratio of AP : PD? 2:310:37:38:326 out of 25Time is Up!