26/03/2020 Geometry(Study by Topics Senior Class) 26/03/2020 0Comments by Gate Academy Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? 2 or 14 1 or 7 4 or 28 3 or 21 2. In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the <span id="MathJax-Element-39-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="ΔACD">ΔACDΔACD and <span id="MathJax-Element-40-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="ΔBCD">ΔBCDΔBCD. P and Q are the centres of the circles. The distance PQ is 8 7 √50 5 3. 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? 45 5 25 85 4. What is the number of distinct triangles with integral valued sides and perimeter 14? 5 6 4 3 5. In <span id="MathJax-Element-22-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="ΔABC">ΔABCΔABC, the internal bisector of <span id="MathJax-Element-23-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="∠A">∠A∠A meets <span id="MathJax-Element-24-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="BC">BCBC at <span id="MathJax-Element-25-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="D">DD. If <span id="MathJax-Element-26-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="AB=4,AC=3and∠A=60∘">AB=4,AC=3 and ∠A=60° AB=4,AC=3 and∠A=60∘, then the length of <span id="MathJax-Element-27-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="AD">ADAD is 2√3 12√3/ 7 15√3/ 8 6√3/ 7 6. 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 7. 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? 120 sq. inches 100 sq. inches 220 sq. inches 200 sq. inches 8. Find the measure of angle A in the figure below. 98° 51° 87° 103° 9. Angles A and B are complementary and the measure of angle A is twice the measure of angle B. Find the measures of angles A and B, A = 60° B = 30° A = 45°, B = 30° A = 30°, B= 45° A = 60°, B = 60° 10. 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 2014 56 11. Which of the following statements is false? An equilateral triangle is also equiangular If two triangles are congruent, then they are also similar If two triangles are similar, then they are also congruent An equiangular triangle is also equilateral 12. A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle? 16.665 14.365 16.565 15.465 13. PQRS is a cyclic quadrilateral and the diagonals PR and QS intersect at T. If <SPR = 47° and <PTQ = 98°,calculate <PRQ 145 degrees 94 degrees 47 degrees 51 degrees 14. When two straight lines intersect I. adjacent angles are equal II. adjacent angles are supplementary III. vertically opposite angles are equalIV. vertically opposite angles are supplementary Which of the above statements are true? I and III only II and III only II and IV only I and IV only 15. 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 is 1:1 n(4-π)/ 4n-π 4n-π/ (4-π) √2:1 16. 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 5 cm 4 cm 2 cm 17. Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centers at P and R respectively, and S is the center of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi-circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to 36 20 28 40 18. 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 √270 √260 √290 √250 19. The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD? π π/2 π/4 3π/2 20. 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 (x+2)/ 8 (4-π)/ 4 (6-π)/ 8 21. Find the area of the given shape. 298 sq. cm 309 sq. cm 183 sq. cm 270 sq. cm 22. Four of the interior angles of a pentagon are specified as (80 - y)°, (80 + y)°, (120 - 2y)° and (120 + 2y)°. The size of the fifth interior angle must be 140 degrees 144 degrees 130 degrees 120 degrees 23. The parallelogram shown in the figure below has a perimeter of 44 cm and an area of 64 cm2. Find angle T in degrees. 64° 55.2° 34.8° 12.3° 24. Find the total surface area of a closed conical container with radius 5 cm and a height of 15 cm. 420 sq. cm 327 sq. cm 209 sq. cm 124 sq. cm 25. 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? 17 m 20 m 15 m 10 m 1 out of 25 Time is Up! Time's up