
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
4Ö2 cm,
length of the other diagonal is? 
Solution: Given
a = 6
cm, b
= 4 cm and d_{1}
= 4Ö2 cm
. d_{2}
= ? 


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
2Ö2 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 = 2Ö2 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 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 ? 









Geometry
and use of trigonometry contents  A 




Copyright
© 2004  2020, Nabla Ltd. All rights reserved. 