26/03/2020Geometry(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 circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?3-2√23-√22+ 2√22-√22. The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is15 cm20 cm25 cm24 cm3. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?1 or 74 or 283 or 212 or 144. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?90150751355. 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 be81π50π40.5π32π6. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC?28°32°84°64°7. If a, b and c are the sides of a triangle, and a^{2}+ b^{2}+ c^{2}= bc + ca + ab, then the triangle isIsoscelesEquilateralobtuse-angledright-angled8. 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 to204036289. 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?ππ/4π/23π/210. 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?90451056011. 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=40^{0}, then ∠ACB =100140702012. 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.35°94°135°148°13. 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/4 -1π/5π/414. The size of angle AOB is equal to 132 degrees and the size of angle COD is equal to 141 degrees. Find the size of angle DOB.23°93°43°53°15. 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?585254516. In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?10 cm50 cm40 cm20 cm17. All the vertices of an isosceles triangle lie on a circle and each of the base angles of the triangle is 65°. The angle subtended at the centre of the circle by the base of the triangle is65 degrees115 degrees100 degrees130 degrees18. 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?16.66514.36516.56515.46519. A cube has a total surface area of the six faces equal to 150 square feet. What is the volume of the cube?673211253520. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?105142121. 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 to1:14:13:23:822. Which of the following statements is false?If two triangles are similar, then they are also congruentAn equilateral triangle is also equiangularAn equiangular triangle is also equilateralIf two triangles are congruent, then they are also similar23. 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 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be020222124. 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 is12 cm20 cm10 cm8 cm25. 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°26 out of 25Time is Up!