Geometry - Plane Figures Problems and Solutions
Plane figures, solved problems, examples
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 circle’s 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 ?
Example:   Into a circle of the radius r inscribed is a square, to the square inscribed is a circle and into the circle inscribed is a square, find the length of the side of the latter square.
Solution:  Given r.    a1 = ?
Example:   Into a sector with R = 9 and a = 60° inscribed is a circle, find the radius of the circle.
Solution:  Given R = 9 and a = 60°.    r = ?
Example:   Two circles with radii 3 cm and 1 cm touch externally. The distance of the point of its contact from their common external tangent is?
Solution:  Given R = 3 cm  and  r = 1 cm.    d = ?
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 = ?
Geometry and use of trigonometry contents - A