
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 D_{1}
and other at D_{2}. Find the length of the segment
D_{1}D_{2}. 
Solution: Given
r_{1}
= 20 cm,
r_{2} =
10 cm and
S_{1}S_{2} =
50 cm . D_{1}D_{2}
= ? 

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.
a_{1}
= ? 

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}
: A_{12}
= ? 









Geometry
and use of trigonometry contents  A 





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