Geometry - Plane Figures Problems and Solutions
      Plane figures, solved problems, examples
Example:   Deltoid with sides length of 1 and 2 is inscribed into a circle. The ratio of greater to the shorter diagonal is?
Solution:  Given  a = 2  and  b = 1.    e :  f = ?
 
Example:   One side of a parallelogram is 4 cm, other 6 cm, and the diagonal 4÷2 cm, length of the other diagonal is?
Solution:  Given  a = 6 cm, b = 4 cm and d1 = 4÷2 cm  .    d2 = ?
 
Example:   Find the area of the rhomb (diamond) with the side of length 20 cm and the diagonal of length 32 cm.
Solution:  Given a = 20 cm and e = 32 cm.    A rhombus = ?
 
Example:   Length of the side of the right decagon is 12. Find the radius of its circumcircle.
Solution:  Given  n = 10 and  a = 12.    r = ?
 
Example:   In a circle with the radius 2 cm, on its chord 2÷2 cm long taken as a diameter, constructed is another circle. The area of the part of that circle, which is outside of the greater circle, is?
Solution:  Given r = 2 cm and t = 2÷2 cm.    A = ?
 
Example:   Distance of centers of circles with radii, 20 cm and 10 cm, is 50 cm. Their common external tangent touches one circle at a point D1 and other at D2. Find the length of the segment D1D2.
Solution:  Given r1 = 20 cm, r2 = 10 cm  and  S1S2 = 50 cm .    D1D2 = ?
 
Example:   The chord of a circle is long 12 cm and cuts of the circle segment whose height is 3 cm. Find the radius of the circle. Height of the segment equals the difference between the radius of the circle and the distance of the chord from the circleís center.
Solution:  Given  t = 12 and h = 3.    r = ?
 
Example:   The perimeter of a circle is divided to the four parts whose arcs relate as 1: 2 : 4 : 5, what are the values of the corresponding central angles?
Solution:  Given arcs relationship, 1: 2 : 4 : 5.    the corresponding central angles ?
 
Geometry and use of trigonometry contents - A
Copyright © 2004 - 2020, Nabla Ltd.  All rights reserved.