Geometry - Plane Figures Problems and Solutions
      Plane figures, solved problems, examples
Example:   The ratio of the area of the circumcircle and the area of the inscribed regular dodecagon is?
Solution:  Given n = 12.    A circle :  A12 = ?
 
Example:   In a circle the chord AB subtends the central angle a and the chord CD subtends the central angle b, if given are, d(AB) = a and angles a and b, then d(CD) is?
Solution:  Given  d(AB) = a, a and b.    d(CD) = ?
 
Example:   The area of the sector A = 64 and the perimeter P = 32, find the length of its arc. 
Solution:  Given A = 64 and P = 32.    arc l = ?
 
Example:   Bases of an isosceles trapezium are, 21 cm and 9 cm, and its height 8 cm. The radius of its circumcircle is?
Solution:  Given a = 21 cm, c = 9 cm  and  h = 8 cm.    r = ?
 
Example:   Find the area of the intersection of two circles with the same radius r = 8 whose centers lay on each other circumferences.
Solution:  Given r = 8.    A intersection = ?
 
Example:   The area of an annulus equals the quarter of the area of the inner circle. The ratio of the radius of the inner circle to the radius of the outer circle is?
Solution:  Given  Aanulus = 1/4 Ar2.    r2 : r1  = ?
 
Example:   The ratio of the radius of the incircle to the radius of the circumcircle of a right triangle with legs, a = 3 and b = 4, is?
Solution:  Given a = 3 and b = 4.    r : R = ?
 
Geometry and use of trigonometry contents - A
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